MakML: Machine Learning Examples in R
W. Evan Johnson
2024-10-31
Set up: load these packages!
library(umap)
library(caret)
library(DT)
library(tidyverse)
library(e1071)
library(gridExtra)
library(mda)
library(randomForest)
library(neuralnet)MakML: Introduction to Machine Learning
Below is the code for the following modules:
- Introduction to R
- Biomarker development
- Dimension Reduction
- Visualizing High Dimensional Data in R
- Support Vector Machines
- Decision Trees and Random Forests
- Neural Networks
- Additional Practice
Introduction to R
To get started, you will need the following dependencies (R packages to install and datasets to download):
- Install R and R Studio
- Please install the following R packages for Data Management:
tidyverse,DT, andgridExtra. In R:
install.packages(c("tidyverse", "DT", "gridExtra"))- Please install the following R packages for Machine learning:
umap,mdacaret,e1071,rpart,randomForest,neuralnet. In R:
install.packages(c("umap","mda","caret", "e1071", "rpart", "randomForest", "neuralnet"))- You will need the following datasets:
heights.rds,olive.rds, andTBnanostring.rds
Data Frames
A large proportion of data analysis challenges start with data stored
in a data frame. For example, we stored the data for our motivating
example in a data frame. You can access this dataset by loading
TBNanostring.rds object in R:
TBnanostring <- readRDS("TBnanostring.rds")In RStudio we can view the data with the View
function:
View(TBnanostring)Or in RMarkdown you can use the datatable function from
the DT package:
datatable(TBnanostring)You will notice that the TB status is found in the first column of the data frame, followed by the genes in the subsequent columns. The rows represent each individual patient.
Dimension Reduction
PCA Example
Here is the code for applying PCA to the Nanostring dataset:
pca_out <- prcomp(TBnanostring[,-1])
names(pca_out)## [1] "sdev" "rotation" "center" "scale" "x"Here is a summary of the explained variation from the PCA:
round(pca_out$sdev^2/sum(pca_out$sdev^2),3)## [1] 0.468 0.073 0.058 0.037 0.033 0.024 0.021 0.018 0.016 0.015 0.013 0.013
## [13] 0.011 0.010 0.009 0.009 0.008 0.008 0.008 0.007 0.007 0.007 0.006 0.006
## [25] 0.006 0.006 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.003 0.003 0.003
## [37] 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
## [49] 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
## [61] 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
## [73] 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [85] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## [97] 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000And the cumulative variation explained:
round(cumsum(pca_out$sdev^2)/sum(pca_out$sdev^2),3)## [1] 0.468 0.541 0.599 0.636 0.669 0.694 0.714 0.732 0.747 0.762 0.776 0.788
## [13] 0.799 0.810 0.819 0.827 0.836 0.844 0.851 0.859 0.866 0.872 0.879 0.885
## [25] 0.891 0.896 0.902 0.906 0.911 0.915 0.919 0.923 0.927 0.931 0.934 0.937
## [37] 0.940 0.943 0.946 0.949 0.951 0.953 0.956 0.958 0.960 0.962 0.964 0.966
## [49] 0.967 0.969 0.971 0.972 0.974 0.975 0.976 0.978 0.979 0.980 0.981 0.982
## [61] 0.983 0.984 0.985 0.986 0.987 0.988 0.988 0.989 0.990 0.990 0.991 0.992
## [73] 0.992 0.993 0.993 0.994 0.994 0.995 0.995 0.995 0.996 0.996 0.997 0.997
## [85] 0.997 0.997 0.998 0.998 0.998 0.998 0.998 0.999 0.999 0.999 0.999 0.999
## [97] 0.999 0.999 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000Now we will make a dataframe with the PCs for later use!
pca_reduction <- as.data.frame(pca_out$x)
pca_reduction$Condition <- as.factor(TBnanostring$TB_Status)
datatable(pca_reduction)UMAP Example
set.seed(0) ## need to set the seed or results might be different
umap_out <- umap(TBnanostring[,-1])
names(umap_out)## [1] "layout" "data" "knn" "config"Now we will make a dataframe with the UMAP results for later use!
umap_reduction <- as.data.frame(umap_out$layout)
umap_reduction$Class <- as.factor(TBnanostring$TB_Status)
datatable(umap_reduction)Visualizing data using ggplot2
Below is a step-by-step tutorial for making PCA and UMAP plots using
ggplot2.
PCA Example
Step 0
We want to make the following plot using ggplot2.
Step 1
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")Step 2
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply PCA
pca_out <- prcomp(TBnanostring[,-1])Step 3
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply PCA
pca_out <- prcomp(TBnanostring[,-1])
## Make a dataframe with the results for plotting
pca_reduction <- as.data.frame(pca_out$x)
pca_reduction$Condition <- as.factor(TBnanostring$TB_Status)Step 4
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply PCA
pca_out <- prcomp(TBnanostring[,-1])
## Make a dataframe with the results for plotting
pca_reduction <- as.data.frame(pca_out$x)
pca_reduction$Condition <- as.factor(TBnanostring$TB_Status)
## Initialize the plot
pca_reduction %>% ggplot()
Step 5
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply PCA
pca_out <- prcomp(TBnanostring[,-1])
## Make a dataframe with the results for plotting
pca_reduction <- as.data.frame(pca_out$x)
pca_reduction$Condition <- as.factor(TBnanostring$TB_Status)
## Add your geometry layer with x and y aesthetics
pca_reduction %>% ggplot() +
geom_point(aes(x=PC1, y=PC2)) 
Step 6
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply PCA
pca_out <- prcomp(TBnanostring[,-1])
## Make a dataframe with the results for plotting
pca_reduction <- as.data.frame(pca_out$x)
pca_reduction$Condition <- as.factor(TBnanostring$TB_Status)
## Change the shape of the points
pca_reduction %>% ggplot() +
geom_point(aes(x=PC1, y=PC2), shape=1) 
Step 7
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply PCA
pca_out <- prcomp(TBnanostring[,-1])
## Make a dataframe with the results for plotting
pca_reduction <- as.data.frame(pca_out$x)
pca_reduction$Condition <- as.factor(TBnanostring$TB_Status)
## Change color of points (add a mapping aesthetic)
pca_reduction %>% ggplot() +
geom_point(aes(x=PC1, y=PC2, color=Condition), shape=1)
Step 8
## Read in the data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply PCA
pca_out <- prcomp(TBnanostring[,-1])
## Make a dataframe with the results for plotting
pca_reduction <- as.data.frame(pca_out$x)
pca_reduction$Condition <- as.factor(TBnanostring$TB_Status)
## Add labels, title, and theme
pca_reduction %>% ggplot() +
geom_point(aes(x=PC1, y=PC2, color=Condition), shape=1) +
xlab("UMAP 1") + ylab("UMAP 2") + ggtitle("UMAP Plot") +
theme(plot.title = element_text(hjust = 0.5)) 
UMAP Example
Here is the final UMAP plot
## Read in data
TBnanostring <- readRDS("TBnanostring.rds")
## Apply UMAP reduction
set.seed(0)
library(umap)
umap_out <- umap(TBnanostring[,-1])
## Make dataframe for plotting in tidy format
umap_reduction <- as.data.frame(umap_out$layout)
umap_reduction$Condition <- as.factor(TBnanostring$TB_Status)
## Plot results with ggpplot
umap_reduction %>% ggplot() +
geom_point(aes(x=V1, y=V2, color=Condition), shape=1) +
xlab("UMAP 1") + ylab("UMAP 2") + ggtitle("UMAP Plot") +
theme(plot.title = element_text(hjust = 0.5)) 
Using the caret package
The caret package in R has several useful functions for
building and assessing machine learning methods. It tries to consolidate
many machine learning tools to provide a consistent syntax.
Using the height data
For a first example, we use the height data in dslabs:
heights <- readRDS("heights.rds")
datatable(heights)boxplot(heights$height ~ heights$sex)
Partition dataset
The caret package includes the function
createDataPartition that helps us generates indexes for
randomly splitting the data into training and test sets:
set.seed(2007)
test_index <- createDataPartition(heights$sex, times = 1,
p = 0.5, list = FALSE)
test_set <- heights[test_index, ]
train_set <- heights[-test_index, ]The argument times is used to define how many random
samples of indexes to return, p is used to define what
proportion of the data is represented by the index, and
list is used to decide if we want the indexes returned as a
list or not.
Simple predictor
Exploratory data analysis suggests we can because, on average, males are slightly taller than females:
heights %>% group_by(sex) %>%
summarize(mean(height), sd(height))## # A tibble: 2 × 3
## sex `mean(height)` `sd(height)`
## <fct> <dbl> <dbl>
## 1 Female 64.9 3.76
## 2 Male 69.3 3.61Let’s try predicting with a simple approach: predict
Male if height is within two standard deviations from the
average male. The overall accuracy is 0.78 in the test set:
pred_test <- ifelse(test_set$height > 62, "Male", "Female") %>%
factor(levels = levels(test_set$sex))
confusionMatrix(pred_test, test_set$sex)## Confusion Matrix and Statistics
##
## Reference
## Prediction Female Male
## Female 22 18
## Male 97 388
##
## Accuracy : 0.781
## 95% CI : (0.7431, 0.8156)
## No Information Rate : 0.7733
## P-Value [Acc > NIR] : 0.3607
##
## Kappa : 0.1836
##
## Mcnemar's Test P-Value : 3.502e-13
##
## Sensitivity : 0.18487
## Specificity : 0.95567
## Pos Pred Value : 0.55000
## Neg Pred Value : 0.80000
## Prevalence : 0.22667
## Detection Rate : 0.04190
## Detection Prevalence : 0.07619
## Balanced Accuracy : 0.57027
##
## 'Positive' Class : Female
## Use the train function
The caret package currently includes 237+ different
machine learning methods, which can be applied using the
train function. These are summarized in the caret
package manual.
Keep in mind that caret does not include the needed
packages and, to implement a package through caret, you
still need to install the library. For example:
height_glm <- train(sex ~ height, method = "glm", data=train_set)
confusionMatrix(predict(height_glm, train_set),
train_set$sex)## Confusion Matrix and Statistics
##
## Reference
## Prediction Female Male
## Female 61 18
## Male 58 388
##
## Accuracy : 0.8552
## 95% CI : (0.8222, 0.8842)
## No Information Rate : 0.7733
## P-Value [Acc > NIR] : 1.679e-06
##
## Kappa : 0.5314
##
## Mcnemar's Test P-Value : 7.691e-06
##
## Sensitivity : 0.5126
## Specificity : 0.9557
## Pos Pred Value : 0.7722
## Neg Pred Value : 0.8700
## Prevalence : 0.2267
## Detection Rate : 0.1162
## Detection Prevalence : 0.1505
## Balanced Accuracy : 0.7341
##
## 'Positive' Class : Female
## SVMs (Linear)
Generate dataset
First generate some data in 2 dimensions, and make them a little separated:
set.seed(10111)
x = matrix(rnorm(40), 20, 2)
y = rep(c(-1, 1), c(10, 10))
x[y == 1,] = x[y == 1,] + 1
plot(x, col = y + 3, pch = 19)
Apply SVM
We will use the e1071 package which contains the
svm function that works on the dataframe (\(y\) needs to be a factor variable).
Printing the svmfit gives its summary.
dat = data.frame(x, y = as.factor(y))
svmfit = svm(y ~ ., data = dat, kernel = "linear", cost = 10, scale = FALSE)
print(svmfit)##
## Call:
## svm(formula = y ~ ., data = dat, kernel = "linear", cost = 10, scale = FALSE)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 10
##
## Number of Support Vectors: 6You can see that the number of support vectors is 6 - they are the points that are close to the boundary or on the wrong side of the boundary.
Plot SVM (version 1)
There’s a generic plot function for SVM that shows the decision boundary, as you can see below. It doesn’t seem there’s much control over the colors. It breaks with convention since it puts x2 on the horizontal axis and x1 on the vertical axis.
plot(svmfit, dat)
Plot SVM (version 2)
Or plotting it more cleanly:
make.grid = function(x, n = 75) {
grange = apply(x, 2, range)
x1 = seq(from = grange[1,1], to = grange[2,1], length = n)
x2 = seq(from = grange[1,2], to = grange[2,2], length = n)
expand.grid(X1 = x1, X2 = x2)
}
xgrid = make.grid(x)ygrid = predict(svmfit, xgrid)
plot(xgrid, col = c("red","blue")[as.numeric(ygrid)], pch = 20, cex = .2)
points(x, col = y + 3, pch = 19)
points(x[svmfit$index,], pch = 5, cex = 2)
Unfortunately, the svm function is not too friendly, in that you have to do some work to get back the linear coefficients. The reason is probably that this only makes sense for linear kernels, and the function is more general. So let’s use a formula to extract the coefficients more efficiently. You extract \(\beta\) and \(\beta_0\), which are the linear coefficients.
beta = drop(t(svmfit$coefs)%*%x[svmfit$index,])
beta0 = svmfit$rhoNow you can replot the points on the grid, then put the points back in (including the support vector points). Then you can use the coefficients to draw the decision boundary using a simple equation of the form:
\[\beta_0+x_1\beta_1+x_2\beta_2=0\]
Now plotting the lines on the graph:
plot(xgrid, col = c("red", "blue")[as.numeric(ygrid)], pch = 20, cex = .2)
points(x, col = y + 3, pch = 19)
points(x[svmfit$index,], pch = 5, cex = 2)
abline(beta0 / beta[2], -beta[1] / beta[2])
abline((beta0 - 1) / beta[2], -beta[1] / beta[2], lty = 2)
abline((beta0 + 1) / beta[2], -beta[1] / beta[2], lty = 2)
SVM Nanostring data
Remember the PCA dimension reduction of the TB Nanostring dataset. The points are colored based on TB status.
Now let’s try an SVM on the PCs of the Nanostring data
# use only the first 2 PCs
dat = data.frame(y = pca_reduction$Condition,
pca_reduction[,1:2])
fit = svm(y ~ ., data = dat, scale = FALSE,
kernel = "linear", cost = 10)
print(fit)##
## Call:
## svm(formula = y ~ ., data = dat, kernel = "linear", cost = 10, scale = FALSE)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: linear
## cost: 10
##
## Number of Support Vectors: 52We can evaluate the predictor with a
Confusion matrix:
confusionMatrix(dat$y,predict(fit,dat))## Confusion Matrix and Statistics
##
## Reference
## Prediction TB LTBI
## TB 69 10
## LTBI 8 92
##
## Accuracy : 0.8994
## 95% CI : (0.8457, 0.9393)
## No Information Rate : 0.5698
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.7955
##
## Mcnemar's Test P-Value : 0.8137
##
## Sensitivity : 0.8961
## Specificity : 0.9020
## Pos Pred Value : 0.8734
## Neg Pred Value : 0.9200
## Prevalence : 0.4302
## Detection Rate : 0.3855
## Detection Prevalence : 0.4413
## Balanced Accuracy : 0.8990
##
## 'Positive' Class : TB
## Plotting Nanostring data:
plot(fit,dat,PC2~PC1)
And plotting the results more cleanly:
SVMs (Non-linear)
Example 1 (polynomial kernel)
Apply polynomial SVM
Now let’s apply a non-linear (polynomial) SVM to our prior simulated dataset.
dat = data.frame(x, y = as.factor(y))
svmfit = svm(y ~ ., data = dat,
kernel = "polynomial", cost = 10, scale = FALSE)
print(svmfit)##
## Call:
## svm(formula = y ~ ., data = dat, kernel = "polynomial", cost = 10,
## scale = FALSE)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: polynomial
## cost: 10
## degree: 3
## coef.0: 0
##
## Number of Support Vectors: 4Plot results
Plotting the result:
Example 2 (radial basis kernel)
Load data
Here is a more complex example from Elements of Statistical
Learning (from the mda R package), where the decision
boundary needs to be non-linear and there is no clear separation.
rm(x,y)
data(ESL.mixture)
attach(ESL.mixture)
names(ESL.mixture)## [1] "x" "y" "xnew" "prob" "marginal" "px1" "px2"
## [8] "means"Plotting the data:
plot(x, col = y + 1)
Apply SVM (radial basis kernel)
Now make a data frame with the response \(y\), and turn that into a factor. We will fit an SVM with radial kernel.
dat = data.frame(y = factor(y), x)
fit = svm(factor(y) ~ ., data = dat, scale = FALSE,
kernel = "radial", cost = 5)
print(fit)##
## Call:
## svm(formula = factor(y) ~ ., data = dat, kernel = "radial", cost = 5,
## scale = FALSE)
##
##
## Parameters:
## SVM-Type: C-classification
## SVM-Kernel: radial
## cost: 5
##
## Number of Support Vectors: 103Plotting the result
It’s time to create a grid and predictions. We use
expand.grid to create the grid, predict each of the values
on the grid, and plot them:
xgrid = expand.grid(X1 = px1, X2 = px2)
ygrid = predict(fit, xgrid)
plot(xgrid, col = as.numeric(ygrid), pch = 20, cex = .2)
points(x, col = y + 1, pch = 19)
Plotting with a contour:
Decision Trees
Olive oil
We will use a new dataset that includes the breakdown of the composition of olive oil into 8 fatty acids:
olive <- readRDS("olive.rds")
olive <- select(olive, -area) #remove the `area` column--don't use it
olive %>% datatable()We will try to predict the region using the fatty acid composition values as predictors.
table(olive$region)##
## Northern Italy Sardinia Southern Italy
## 151 98 323Boxplots
A bit of data exploration reveals that we should be able to do even better: note that eicosenoic is only in Southern Italy and linoleic separates Northern Italy from Sardinia.
olive %>% gather(fatty_acid, percentage, -region) %>%
ggplot(aes(region, percentage, fill = region)) +
geom_boxplot() +
facet_wrap(~fatty_acid, scales = "free", ncol = 4) +
theme(axis.text.x = element_blank(), legend.position="bottom")
Paritions
This implies that we should be able to build an algorithm that predicts perfectly! Let’s try plotting the values for eicosenoic and linoleic.
olive %>%
ggplot(aes(eicosenoic, linoleic, color = region)) +
geom_point(size=2) +
geom_vline(xintercept = 0.065, lty = 2) +
geom_segment(x = -0.2, y = 10.54, xend = 0.065, yend = 10.54,
color = "black", lty = 2)
Decision tree
Let’s define a decision rule: If eicosenoic is larger than 0.065, predict Southern Italy. If not, then if linoleic is larger than \(10.535\), predict Sardinia, otherwise predict Northern Italy. We can draw this decision tree:
train_rpart <- train(region ~ ., method = "rpart", data = olive)
plot(train_rpart$finalModel, margin = 0.1)
text(train_rpart$finalModel, cex = 0.75)
Random Forests
Summarize data
For this example we will use the Iris data in R
datatable(iris)iris %>% ggplot(aes(Petal.Width, Petal.Length, color = Species)) +
geom_point()
Select train/test
set.seed(0)
test_index <- createDataPartition(iris$Species, times = 1,
p = 0.3, list = FALSE)
iris_test <- iris[test_index, ]
iris_train <- iris[-test_index, ]Apply Random Forest
iris_classifier <- randomForest(Species~., data = iris_train,
importance=T)
iris_classifier##
## Call:
## randomForest(formula = Species ~ ., data = iris_train, importance = T)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 2
##
## OOB estimate of error rate: 2.86%
## Confusion matrix:
## setosa versicolor virginica class.error
## setosa 35 0 0 0.00000000
## versicolor 0 34 1 0.02857143
## virginica 0 2 33 0.05714286Results summary
plot(iris_classifier)
importance(iris_classifier)## setosa versicolor virginica MeanDecreaseAccuracy
## Sepal.Length 6.247640 8.383367 5.865249 10.618792
## Sepal.Width 4.490071 3.098781 3.295522 5.011737
## Petal.Length 22.641994 36.724624 25.382407 34.376688
## Petal.Width 21.561037 31.744843 24.616309 30.800022
## MeanDecreaseGini
## Sepal.Length 5.527267
## Sepal.Width 1.786515
## Petal.Length 31.838258
## Petal.Width 30.130208varImpPlot(iris_classifier)
Predictions
predicted_table <- predict(iris_classifier, iris_test[,-5])
confusionMatrix(predicted_table, iris_test[,5])## Confusion Matrix and Statistics
##
## Reference
## Prediction setosa versicolor virginica
## setosa 15 0 0
## versicolor 0 13 1
## virginica 0 2 14
##
## Overall Statistics
##
## Accuracy : 0.9333
## 95% CI : (0.8173, 0.986)
## No Information Rate : 0.3333
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: setosa Class: versicolor Class: virginica
## Sensitivity 1.0000 0.8667 0.9333
## Specificity 1.0000 0.9667 0.9333
## Pos Pred Value 1.0000 0.9286 0.8750
## Neg Pred Value 1.0000 0.9355 0.9655
## Prevalence 0.3333 0.3333 0.3333
## Detection Rate 0.3333 0.2889 0.3111
## Detection Prevalence 0.3333 0.3111 0.3556
## Balanced Accuracy 1.0000 0.9167 0.9333Neural Networks
Example 1: Job Placement
Placement data (toy example)
Suppose we have students’ technical knowledge (TKS), communication skill score (CSS), and placement status (Placed):
TKS=c(20,10,30,20,80,30)
CSS=c(90,20,40,50,50,80)
Placed=c(1,0,0,0,1,1)
df=data.frame(TKS,CSS,Placed)
datatable(df)Fit Neural Network
Fit the multilayer perceptron neural network:
set.seed(0)
nn=neuralnet::neuralnet(Placed~TKS+CSS,data=df, hidden=3,
act.fct = "logistic", linear.output = FALSE)
names(nn)## [1] "call" "response" "covariate"
## [4] "model.list" "err.fct" "act.fct"
## [7] "linear.output" "data" "exclude"
## [10] "net.result" "weights" "generalized.weights"
## [13] "startweights" "result.matrix"Plot Neural Network
We can plot or neural network:
plot(nn, rep="best")
Predictions
Creating a test set:
TKS=c(30,40,85)
CSS=c(85,50,40)
test=data.frame(TKS,CSS)
datatable(test)pred_nn = neuralnet::compute(nn,test)$net.result
pred_class <- ifelse(pred_nn>0.45, 1, 0)
pred_class## [,1]
## [1,] 0
## [2,] 0
## [3,] 1Example 2: Iris data
NN on Iris data
Now, using the iris dataset:
set.seed(0)
nn_iris <- neuralnet(Species ~ ., data=iris, hidden=3)
nn_iris## $call
## neuralnet(formula = Species ~ ., data = iris, hidden = 3)
##
## $response
## setosa versicolor virginica
## 1 TRUE FALSE FALSE
## 2 TRUE FALSE FALSE
## 3 TRUE FALSE FALSE
## 4 TRUE FALSE FALSE
## 5 TRUE FALSE FALSE
## 6 TRUE FALSE FALSE
## 7 TRUE FALSE FALSE
## 8 TRUE FALSE FALSE
## 9 TRUE FALSE FALSE
## 10 TRUE FALSE FALSE
## 11 TRUE FALSE FALSE
## 12 TRUE FALSE FALSE
## 13 TRUE FALSE FALSE
## 14 TRUE FALSE FALSE
## 15 TRUE FALSE FALSE
## 16 TRUE FALSE FALSE
## 17 TRUE FALSE FALSE
## 18 TRUE FALSE FALSE
## 19 TRUE FALSE FALSE
## 20 TRUE FALSE FALSE
## 21 TRUE FALSE FALSE
## 22 TRUE FALSE FALSE
## 23 TRUE FALSE FALSE
## 24 TRUE FALSE FALSE
## 25 TRUE FALSE FALSE
## 26 TRUE FALSE FALSE
## 27 TRUE FALSE FALSE
## 28 TRUE FALSE FALSE
## 29 TRUE FALSE FALSE
## 30 TRUE FALSE FALSE
## 31 TRUE FALSE FALSE
## 32 TRUE FALSE FALSE
## 33 TRUE FALSE FALSE
## 34 TRUE FALSE FALSE
## 35 TRUE FALSE FALSE
## 36 TRUE FALSE FALSE
## 37 TRUE FALSE FALSE
## 38 TRUE FALSE FALSE
## 39 TRUE FALSE FALSE
## 40 TRUE FALSE FALSE
## 41 TRUE FALSE FALSE
## 42 TRUE FALSE FALSE
## 43 TRUE FALSE FALSE
## 44 TRUE FALSE FALSE
## 45 TRUE FALSE FALSE
## 46 TRUE FALSE FALSE
## 47 TRUE FALSE FALSE
## 48 TRUE FALSE FALSE
## 49 TRUE FALSE FALSE
## 50 TRUE FALSE FALSE
## 51 FALSE TRUE FALSE
## 52 FALSE TRUE FALSE
## 53 FALSE TRUE FALSE
## 54 FALSE TRUE FALSE
## 55 FALSE TRUE FALSE
## 56 FALSE TRUE FALSE
## 57 FALSE TRUE FALSE
## 58 FALSE TRUE FALSE
## 59 FALSE TRUE FALSE
## 60 FALSE TRUE FALSE
## 61 FALSE TRUE FALSE
## 62 FALSE TRUE FALSE
## 63 FALSE TRUE FALSE
## 64 FALSE TRUE FALSE
## 65 FALSE TRUE FALSE
## 66 FALSE TRUE FALSE
## 67 FALSE TRUE FALSE
## 68 FALSE TRUE FALSE
## 69 FALSE TRUE FALSE
## 70 FALSE TRUE FALSE
## 71 FALSE TRUE FALSE
## 72 FALSE TRUE FALSE
## 73 FALSE TRUE FALSE
## 74 FALSE TRUE FALSE
## 75 FALSE TRUE FALSE
## 76 FALSE TRUE FALSE
## 77 FALSE TRUE FALSE
## 78 FALSE TRUE FALSE
## 79 FALSE TRUE FALSE
## 80 FALSE TRUE FALSE
## 81 FALSE TRUE FALSE
## 82 FALSE TRUE FALSE
## 83 FALSE TRUE FALSE
## 84 FALSE TRUE FALSE
## 85 FALSE TRUE FALSE
## 86 FALSE TRUE FALSE
## 87 FALSE TRUE FALSE
## 88 FALSE TRUE FALSE
## 89 FALSE TRUE FALSE
## 90 FALSE TRUE FALSE
## 91 FALSE TRUE FALSE
## 92 FALSE TRUE FALSE
## 93 FALSE TRUE FALSE
## 94 FALSE TRUE FALSE
## 95 FALSE TRUE FALSE
## 96 FALSE TRUE FALSE
## 97 FALSE TRUE FALSE
## 98 FALSE TRUE FALSE
## 99 FALSE TRUE FALSE
## 100 FALSE TRUE FALSE
## 101 FALSE FALSE TRUE
## 102 FALSE FALSE TRUE
## 103 FALSE FALSE TRUE
## 104 FALSE FALSE TRUE
## 105 FALSE FALSE TRUE
## 106 FALSE FALSE TRUE
## 107 FALSE FALSE TRUE
## 108 FALSE FALSE TRUE
## 109 FALSE FALSE TRUE
## 110 FALSE FALSE TRUE
## 111 FALSE FALSE TRUE
## 112 FALSE FALSE TRUE
## 113 FALSE FALSE TRUE
## 114 FALSE FALSE TRUE
## 115 FALSE FALSE TRUE
## 116 FALSE FALSE TRUE
## 117 FALSE FALSE TRUE
## 118 FALSE FALSE TRUE
## 119 FALSE FALSE TRUE
## 120 FALSE FALSE TRUE
## 121 FALSE FALSE TRUE
## 122 FALSE FALSE TRUE
## 123 FALSE FALSE TRUE
## 124 FALSE FALSE TRUE
## 125 FALSE FALSE TRUE
## 126 FALSE FALSE TRUE
## 127 FALSE FALSE TRUE
## 128 FALSE FALSE TRUE
## 129 FALSE FALSE TRUE
## 130 FALSE FALSE TRUE
## 131 FALSE FALSE TRUE
## 132 FALSE FALSE TRUE
## 133 FALSE FALSE TRUE
## 134 FALSE FALSE TRUE
## 135 FALSE FALSE TRUE
## 136 FALSE FALSE TRUE
## 137 FALSE FALSE TRUE
## 138 FALSE FALSE TRUE
## 139 FALSE FALSE TRUE
## 140 FALSE FALSE TRUE
## 141 FALSE FALSE TRUE
## 142 FALSE FALSE TRUE
## 143 FALSE FALSE TRUE
## 144 FALSE FALSE TRUE
## 145 FALSE FALSE TRUE
## 146 FALSE FALSE TRUE
## 147 FALSE FALSE TRUE
## 148 FALSE FALSE TRUE
## 149 FALSE FALSE TRUE
## 150 FALSE FALSE TRUE
##
## $covariate
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## [1,] 5.1 3.5 1.4 0.2
## [2,] 4.9 3.0 1.4 0.2
## [3,] 4.7 3.2 1.3 0.2
## [4,] 4.6 3.1 1.5 0.2
## [5,] 5.0 3.6 1.4 0.2
## [6,] 5.4 3.9 1.7 0.4
## [7,] 4.6 3.4 1.4 0.3
## [8,] 5.0 3.4 1.5 0.2
## [9,] 4.4 2.9 1.4 0.2
## [10,] 4.9 3.1 1.5 0.1
## [11,] 5.4 3.7 1.5 0.2
## [12,] 4.8 3.4 1.6 0.2
## [13,] 4.8 3.0 1.4 0.1
## [14,] 4.3 3.0 1.1 0.1
## [15,] 5.8 4.0 1.2 0.2
## [16,] 5.7 4.4 1.5 0.4
## [17,] 5.4 3.9 1.3 0.4
## [18,] 5.1 3.5 1.4 0.3
## [19,] 5.7 3.8 1.7 0.3
## [20,] 5.1 3.8 1.5 0.3
## [21,] 5.4 3.4 1.7 0.2
## [22,] 5.1 3.7 1.5 0.4
## [23,] 4.6 3.6 1.0 0.2
## [24,] 5.1 3.3 1.7 0.5
## [25,] 4.8 3.4 1.9 0.2
## [26,] 5.0 3.0 1.6 0.2
## [27,] 5.0 3.4 1.6 0.4
## [28,] 5.2 3.5 1.5 0.2
## [29,] 5.2 3.4 1.4 0.2
## [30,] 4.7 3.2 1.6 0.2
## [31,] 4.8 3.1 1.6 0.2
## [32,] 5.4 3.4 1.5 0.4
## [33,] 5.2 4.1 1.5 0.1
## [34,] 5.5 4.2 1.4 0.2
## [35,] 4.9 3.1 1.5 0.2
## [36,] 5.0 3.2 1.2 0.2
## [37,] 5.5 3.5 1.3 0.2
## [38,] 4.9 3.6 1.4 0.1
## [39,] 4.4 3.0 1.3 0.2
## [40,] 5.1 3.4 1.5 0.2
## [41,] 5.0 3.5 1.3 0.3
## [42,] 4.5 2.3 1.3 0.3
## [43,] 4.4 3.2 1.3 0.2
## [44,] 5.0 3.5 1.6 0.6
## [45,] 5.1 3.8 1.9 0.4
## [46,] 4.8 3.0 1.4 0.3
## [47,] 5.1 3.8 1.6 0.2
## [48,] 4.6 3.2 1.4 0.2
## [49,] 5.3 3.7 1.5 0.2
## [50,] 5.0 3.3 1.4 0.2
## [51,] 7.0 3.2 4.7 1.4
## [52,] 6.4 3.2 4.5 1.5
## [53,] 6.9 3.1 4.9 1.5
## [54,] 5.5 2.3 4.0 1.3
## [55,] 6.5 2.8 4.6 1.5
## [56,] 5.7 2.8 4.5 1.3
## [57,] 6.3 3.3 4.7 1.6
## [58,] 4.9 2.4 3.3 1.0
## [59,] 6.6 2.9 4.6 1.3
## [60,] 5.2 2.7 3.9 1.4
## [61,] 5.0 2.0 3.5 1.0
## [62,] 5.9 3.0 4.2 1.5
## [63,] 6.0 2.2 4.0 1.0
## [64,] 6.1 2.9 4.7 1.4
## [65,] 5.6 2.9 3.6 1.3
## [66,] 6.7 3.1 4.4 1.4
## [67,] 5.6 3.0 4.5 1.5
## [68,] 5.8 2.7 4.1 1.0
## [69,] 6.2 2.2 4.5 1.5
## [70,] 5.6 2.5 3.9 1.1
## [71,] 5.9 3.2 4.8 1.8
## [72,] 6.1 2.8 4.0 1.3
## [73,] 6.3 2.5 4.9 1.5
## [74,] 6.1 2.8 4.7 1.2
## [75,] 6.4 2.9 4.3 1.3
## [76,] 6.6 3.0 4.4 1.4
## [77,] 6.8 2.8 4.8 1.4
## [78,] 6.7 3.0 5.0 1.7
## [79,] 6.0 2.9 4.5 1.5
## [80,] 5.7 2.6 3.5 1.0
## [81,] 5.5 2.4 3.8 1.1
## [82,] 5.5 2.4 3.7 1.0
## [83,] 5.8 2.7 3.9 1.2
## [84,] 6.0 2.7 5.1 1.6
## [85,] 5.4 3.0 4.5 1.5
## [86,] 6.0 3.4 4.5 1.6
## [87,] 6.7 3.1 4.7 1.5
## [88,] 6.3 2.3 4.4 1.3
## [89,] 5.6 3.0 4.1 1.3
## [90,] 5.5 2.5 4.0 1.3
## [91,] 5.5 2.6 4.4 1.2
## [92,] 6.1 3.0 4.6 1.4
## [93,] 5.8 2.6 4.0 1.2
## [94,] 5.0 2.3 3.3 1.0
## [95,] 5.6 2.7 4.2 1.3
## [96,] 5.7 3.0 4.2 1.2
## [97,] 5.7 2.9 4.2 1.3
## [98,] 6.2 2.9 4.3 1.3
## [99,] 5.1 2.5 3.0 1.1
## [100,] 5.7 2.8 4.1 1.3
## [101,] 6.3 3.3 6.0 2.5
## [102,] 5.8 2.7 5.1 1.9
## [103,] 7.1 3.0 5.9 2.1
## [104,] 6.3 2.9 5.6 1.8
## [105,] 6.5 3.0 5.8 2.2
## [106,] 7.6 3.0 6.6 2.1
## [107,] 4.9 2.5 4.5 1.7
## [108,] 7.3 2.9 6.3 1.8
## [109,] 6.7 2.5 5.8 1.8
## [110,] 7.2 3.6 6.1 2.5
## [111,] 6.5 3.2 5.1 2.0
## [112,] 6.4 2.7 5.3 1.9
## [113,] 6.8 3.0 5.5 2.1
## [114,] 5.7 2.5 5.0 2.0
## [115,] 5.8 2.8 5.1 2.4
## [116,] 6.4 3.2 5.3 2.3
## [117,] 6.5 3.0 5.5 1.8
## [118,] 7.7 3.8 6.7 2.2
## [119,] 7.7 2.6 6.9 2.3
## [120,] 6.0 2.2 5.0 1.5
## [121,] 6.9 3.2 5.7 2.3
## [122,] 5.6 2.8 4.9 2.0
## [123,] 7.7 2.8 6.7 2.0
## [124,] 6.3 2.7 4.9 1.8
## [125,] 6.7 3.3 5.7 2.1
## [126,] 7.2 3.2 6.0 1.8
## [127,] 6.2 2.8 4.8 1.8
## [128,] 6.1 3.0 4.9 1.8
## [129,] 6.4 2.8 5.6 2.1
## [130,] 7.2 3.0 5.8 1.6
## [131,] 7.4 2.8 6.1 1.9
## [132,] 7.9 3.8 6.4 2.0
## [133,] 6.4 2.8 5.6 2.2
## [134,] 6.3 2.8 5.1 1.5
## [135,] 6.1 2.6 5.6 1.4
## [136,] 7.7 3.0 6.1 2.3
## [137,] 6.3 3.4 5.6 2.4
## [138,] 6.4 3.1 5.5 1.8
## [139,] 6.0 3.0 4.8 1.8
## [140,] 6.9 3.1 5.4 2.1
## [141,] 6.7 3.1 5.6 2.4
## [142,] 6.9 3.1 5.1 2.3
## [143,] 5.8 2.7 5.1 1.9
## [144,] 6.8 3.2 5.9 2.3
## [145,] 6.7 3.3 5.7 2.5
## [146,] 6.7 3.0 5.2 2.3
## [147,] 6.3 2.5 5.0 1.9
## [148,] 6.5 3.0 5.2 2.0
## [149,] 6.2 3.4 5.4 2.3
## [150,] 5.9 3.0 5.1 1.8
##
## $model.list
## $model.list$response
## [1] "setosa" "versicolor" "virginica"
##
## $model.list$variables
## [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width"
##
##
## $err.fct
## function (x, y)
## {
## 1/2 * (y - x)^2
## }
## <bytecode: 0x12b7c9af0>
## <environment: 0x11c810630>
## attr(,"type")
## [1] "sse"
##
## $act.fct
## function (x)
## {
## 1/(1 + exp(-x))
## }
## <bytecode: 0x12b7ce490>
## <environment: 0x11c814070>
## attr(,"type")
## [1] "logistic"
##
## $linear.output
## [1] TRUE
##
## $data
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1 5.1 3.5 1.4 0.2 setosa
## 2 4.9 3.0 1.4 0.2 setosa
## 3 4.7 3.2 1.3 0.2 setosa
## 4 4.6 3.1 1.5 0.2 setosa
## 5 5.0 3.6 1.4 0.2 setosa
## 6 5.4 3.9 1.7 0.4 setosa
## 7 4.6 3.4 1.4 0.3 setosa
## 8 5.0 3.4 1.5 0.2 setosa
## 9 4.4 2.9 1.4 0.2 setosa
## 10 4.9 3.1 1.5 0.1 setosa
## 11 5.4 3.7 1.5 0.2 setosa
## 12 4.8 3.4 1.6 0.2 setosa
## 13 4.8 3.0 1.4 0.1 setosa
## 14 4.3 3.0 1.1 0.1 setosa
## 15 5.8 4.0 1.2 0.2 setosa
## 16 5.7 4.4 1.5 0.4 setosa
## 17 5.4 3.9 1.3 0.4 setosa
## 18 5.1 3.5 1.4 0.3 setosa
## 19 5.7 3.8 1.7 0.3 setosa
## 20 5.1 3.8 1.5 0.3 setosa
## 21 5.4 3.4 1.7 0.2 setosa
## 22 5.1 3.7 1.5 0.4 setosa
## 23 4.6 3.6 1.0 0.2 setosa
## 24 5.1 3.3 1.7 0.5 setosa
## 25 4.8 3.4 1.9 0.2 setosa
## 26 5.0 3.0 1.6 0.2 setosa
## 27 5.0 3.4 1.6 0.4 setosa
## 28 5.2 3.5 1.5 0.2 setosa
## 29 5.2 3.4 1.4 0.2 setosa
## 30 4.7 3.2 1.6 0.2 setosa
## 31 4.8 3.1 1.6 0.2 setosa
## 32 5.4 3.4 1.5 0.4 setosa
## 33 5.2 4.1 1.5 0.1 setosa
## 34 5.5 4.2 1.4 0.2 setosa
## 35 4.9 3.1 1.5 0.2 setosa
## 36 5.0 3.2 1.2 0.2 setosa
## 37 5.5 3.5 1.3 0.2 setosa
## 38 4.9 3.6 1.4 0.1 setosa
## 39 4.4 3.0 1.3 0.2 setosa
## 40 5.1 3.4 1.5 0.2 setosa
## 41 5.0 3.5 1.3 0.3 setosa
## 42 4.5 2.3 1.3 0.3 setosa
## 43 4.4 3.2 1.3 0.2 setosa
## 44 5.0 3.5 1.6 0.6 setosa
## 45 5.1 3.8 1.9 0.4 setosa
## 46 4.8 3.0 1.4 0.3 setosa
## 47 5.1 3.8 1.6 0.2 setosa
## 48 4.6 3.2 1.4 0.2 setosa
## 49 5.3 3.7 1.5 0.2 setosa
## 50 5.0 3.3 1.4 0.2 setosa
## 51 7.0 3.2 4.7 1.4 versicolor
## 52 6.4 3.2 4.5 1.5 versicolor
## 53 6.9 3.1 4.9 1.5 versicolor
## 54 5.5 2.3 4.0 1.3 versicolor
## 55 6.5 2.8 4.6 1.5 versicolor
## 56 5.7 2.8 4.5 1.3 versicolor
## 57 6.3 3.3 4.7 1.6 versicolor
## 58 4.9 2.4 3.3 1.0 versicolor
## 59 6.6 2.9 4.6 1.3 versicolor
## 60 5.2 2.7 3.9 1.4 versicolor
## 61 5.0 2.0 3.5 1.0 versicolor
## 62 5.9 3.0 4.2 1.5 versicolor
## 63 6.0 2.2 4.0 1.0 versicolor
## 64 6.1 2.9 4.7 1.4 versicolor
## 65 5.6 2.9 3.6 1.3 versicolor
## 66 6.7 3.1 4.4 1.4 versicolor
## 67 5.6 3.0 4.5 1.5 versicolor
## 68 5.8 2.7 4.1 1.0 versicolor
## 69 6.2 2.2 4.5 1.5 versicolor
## 70 5.6 2.5 3.9 1.1 versicolor
## 71 5.9 3.2 4.8 1.8 versicolor
## 72 6.1 2.8 4.0 1.3 versicolor
## 73 6.3 2.5 4.9 1.5 versicolor
## 74 6.1 2.8 4.7 1.2 versicolor
## 75 6.4 2.9 4.3 1.3 versicolor
## 76 6.6 3.0 4.4 1.4 versicolor
## 77 6.8 2.8 4.8 1.4 versicolor
## 78 6.7 3.0 5.0 1.7 versicolor
## 79 6.0 2.9 4.5 1.5 versicolor
## 80 5.7 2.6 3.5 1.0 versicolor
## 81 5.5 2.4 3.8 1.1 versicolor
## 82 5.5 2.4 3.7 1.0 versicolor
## 83 5.8 2.7 3.9 1.2 versicolor
## 84 6.0 2.7 5.1 1.6 versicolor
## 85 5.4 3.0 4.5 1.5 versicolor
## 86 6.0 3.4 4.5 1.6 versicolor
## 87 6.7 3.1 4.7 1.5 versicolor
## 88 6.3 2.3 4.4 1.3 versicolor
## 89 5.6 3.0 4.1 1.3 versicolor
## 90 5.5 2.5 4.0 1.3 versicolor
## 91 5.5 2.6 4.4 1.2 versicolor
## 92 6.1 3.0 4.6 1.4 versicolor
## 93 5.8 2.6 4.0 1.2 versicolor
## 94 5.0 2.3 3.3 1.0 versicolor
## 95 5.6 2.7 4.2 1.3 versicolor
## 96 5.7 3.0 4.2 1.2 versicolor
## 97 5.7 2.9 4.2 1.3 versicolor
## 98 6.2 2.9 4.3 1.3 versicolor
## 99 5.1 2.5 3.0 1.1 versicolor
## 100 5.7 2.8 4.1 1.3 versicolor
## 101 6.3 3.3 6.0 2.5 virginica
## 102 5.8 2.7 5.1 1.9 virginica
## 103 7.1 3.0 5.9 2.1 virginica
## 104 6.3 2.9 5.6 1.8 virginica
## 105 6.5 3.0 5.8 2.2 virginica
## 106 7.6 3.0 6.6 2.1 virginica
## 107 4.9 2.5 4.5 1.7 virginica
## 108 7.3 2.9 6.3 1.8 virginica
## 109 6.7 2.5 5.8 1.8 virginica
## 110 7.2 3.6 6.1 2.5 virginica
## 111 6.5 3.2 5.1 2.0 virginica
## 112 6.4 2.7 5.3 1.9 virginica
## 113 6.8 3.0 5.5 2.1 virginica
## 114 5.7 2.5 5.0 2.0 virginica
## 115 5.8 2.8 5.1 2.4 virginica
## 116 6.4 3.2 5.3 2.3 virginica
## 117 6.5 3.0 5.5 1.8 virginica
## 118 7.7 3.8 6.7 2.2 virginica
## 119 7.7 2.6 6.9 2.3 virginica
## 120 6.0 2.2 5.0 1.5 virginica
## 121 6.9 3.2 5.7 2.3 virginica
## 122 5.6 2.8 4.9 2.0 virginica
## 123 7.7 2.8 6.7 2.0 virginica
## 124 6.3 2.7 4.9 1.8 virginica
## 125 6.7 3.3 5.7 2.1 virginica
## 126 7.2 3.2 6.0 1.8 virginica
## 127 6.2 2.8 4.8 1.8 virginica
## 128 6.1 3.0 4.9 1.8 virginica
## 129 6.4 2.8 5.6 2.1 virginica
## 130 7.2 3.0 5.8 1.6 virginica
## 131 7.4 2.8 6.1 1.9 virginica
## 132 7.9 3.8 6.4 2.0 virginica
## 133 6.4 2.8 5.6 2.2 virginica
## 134 6.3 2.8 5.1 1.5 virginica
## 135 6.1 2.6 5.6 1.4 virginica
## 136 7.7 3.0 6.1 2.3 virginica
## 137 6.3 3.4 5.6 2.4 virginica
## 138 6.4 3.1 5.5 1.8 virginica
## 139 6.0 3.0 4.8 1.8 virginica
## 140 6.9 3.1 5.4 2.1 virginica
## 141 6.7 3.1 5.6 2.4 virginica
## 142 6.9 3.1 5.1 2.3 virginica
## 143 5.8 2.7 5.1 1.9 virginica
## 144 6.8 3.2 5.9 2.3 virginica
## 145 6.7 3.3 5.7 2.5 virginica
## 146 6.7 3.0 5.2 2.3 virginica
## 147 6.3 2.5 5.0 1.9 virginica
## 148 6.5 3.0 5.2 2.0 virginica
## 149 6.2 3.4 5.4 2.3 virginica
## 150 5.9 3.0 5.1 1.8 virginica
##
## $exclude
## NULL
##
## $net.result
## $net.result[[1]]
## [,1] [,2] [,3]
## [1,] 1.000000e+00 -5.841901e-05 0.0001129900
## [2,] 1.000000e+00 -5.839920e-05 0.0001129693
## [3,] 1.000000e+00 -5.841043e-05 0.0001129811
## [4,] 1.000000e+00 -5.838990e-05 0.0001129596
## [5,] 1.000000e+00 -5.842000e-05 0.0001129911
## [6,] 1.000000e+00 -5.840648e-05 0.0001129770
## [7,] 1.000000e+00 -5.839817e-05 0.0001129683
## [8,] 1.000000e+00 -5.841311e-05 0.0001129839
## [9,] 1.000000e+00 -5.837457e-05 0.0001129436
## [10,] 1.000000e+00 -5.841191e-05 0.0001129826
## [11,] 1.000000e+00 -5.842180e-05 0.0001129930
## [12,] 1.000000e+00 -5.840584e-05 0.0001129763
## [13,] 1.000000e+00 -5.841120e-05 0.0001129819
## [14,] 1.000000e+00 -5.841577e-05 0.0001129867
## [15,] 1.000000e+00 -5.842609e-05 0.0001129974
## [16,] 1.000000e+00 -5.842373e-05 0.0001129950
## [17,] 1.000000e+00 -5.841956e-05 0.0001129906
## [18,] 1.000000e+00 -5.841171e-05 0.0001129824
## [19,] 1.000000e+00 -5.841665e-05 0.0001129876
## [20,] 1.000000e+00 -5.841670e-05 0.0001129876
## [21,] 1.000000e+00 -5.841050e-05 0.0001129812
## [22,] 1.000000e+00 -5.840253e-05 0.0001129728
## [23,] 1.000000e+00 -5.842345e-05 0.0001129947
## [24,] 1.000000e+00 -5.824278e-05 0.0001128058
## [25,] 1.000000e+00 -5.838176e-05 0.0001129511
## [26,] 1.000000e+00 -5.838455e-05 0.0001129540
## [27,] 1.000000e+00 -5.836150e-05 0.0001129299
## [28,] 1.000000e+00 -5.841753e-05 0.0001129885
## [29,] 1.000000e+00 -5.841788e-05 0.0001129889
## [30,] 1.000000e+00 -5.839157e-05 0.0001129614
## [31,] 1.000000e+00 -5.838656e-05 0.0001129561
## [32,] 1.000000e+00 -5.839062e-05 0.0001129604
## [33,] 1.000000e+00 -5.842565e-05 0.0001129970
## [34,] 1.000000e+00 -5.842574e-05 0.0001129971
## [35,] 1.000000e+00 -5.839813e-05 0.0001129682
## [36,] 1.000000e+00 -5.841700e-05 0.0001129879
## [37,] 1.000000e+00 -5.842256e-05 0.0001129938
## [38,] 1.000000e+00 -5.842302e-05 0.0001129942
## [39,] 1.000000e+00 -5.839421e-05 0.0001129641
## [40,] 1.000000e+00 -5.841422e-05 0.0001129850
## [41,] 1.000000e+00 -5.841410e-05 0.0001129849
## [42,] 1.000000e+00 -5.816556e-05 0.0001127251
## [43,] 1.000000e+00 -5.840571e-05 0.0001129761
## [44,] 1.000000e+00 -5.823388e-05 0.0001127965
## [45,] 1.000000e+00 -5.837268e-05 0.0001129416
## [46,] 1.000000e+00 -5.836917e-05 0.0001129380
## [47,] 1.000000e+00 -5.842006e-05 0.0001129911
## [48,] 1.000000e+00 -5.840379e-05 0.0001129741
## [49,] 1.000000e+00 -5.842135e-05 0.0001129925
## [50,] 1.000000e+00 -5.841362e-05 0.0001129844
## [51,] -2.472862e-09 1.000559e+00 -0.0003288359
## [52,] 8.910387e-09 1.013268e+00 -0.0138986863
## [53,] 2.867558e-08 1.020231e+00 -0.0223577880
## [54,] 1.167077e-08 1.015363e+00 -0.0162027429
## [55,] 3.726995e-08 1.024179e+00 -0.0269563294
## [56,] 1.047319e-08 1.010832e+00 -0.0115809831
## [57,] 3.679281e-08 1.023834e+00 -0.0265751513
## [58,] -1.639820e-08 9.818170e-01 0.0194670214
## [59,] -1.601906e-09 1.001161e+00 -0.0009959583
## [60,] 7.345391e-09 1.012197e+00 -0.0127089579
## [61,] -1.332268e-08 9.864060e-01 0.0146454147
## [62,] 1.137538e-08 1.016498e+00 -0.0173153222
## [63,] -1.336366e-08 9.862942e-01 0.0147602277
## [64,] 2.548008e-08 1.015460e+00 -0.0173451239
## [65,] -1.416892e-08 9.852565e-01 0.0158589302
## [66,] -5.781792e-09 9.968169e-01 0.0036641077
## [67,] 3.719424e-08 1.016613e+00 -0.0193850835
## [68,] -1.537609e-08 9.833384e-01 0.0178683047
## [69,] 5.496306e-08 8.593075e-01 0.1365632612
## [70,] -1.299355e-08 9.868585e-01 0.0141679607
## [71,] 1.384538e-08 5.300979e-01 0.4688637496
## [72,] -1.020511e-08 9.909329e-01 0.0098827234
## [73,] 2.263677e-08 6.945533e-01 0.3037541328
## [74,] 1.161969e-09 1.002487e+00 -0.0025311070
## [75,] -8.000526e-09 9.937768e-01 0.0068720379
## [76,] -2.179031e-09 1.001279e+00 -0.0010703936
## [77,] 2.326898e-08 1.018265e+00 -0.0199826773
## [78,] 3.336351e-08 6.907487e-01 0.3067460681
## [79,] 3.511165e-08 1.023062e+00 -0.0256764701
## [80,] -1.695645e-08 9.809399e-01 0.0203862656
## [81,] -1.277217e-08 9.871959e-01 0.0138138443
## [82,] -1.559605e-08 9.830375e-01 0.0181858442
## [83,] -1.272993e-08 9.872975e-01 0.0137090869
## [84,] -5.246270e-08 2.095318e-01 0.7944291224
## [85,] 4.083709e-08 1.007550e+00 -0.0105988419
## [86,] 2.311256e-08 1.024348e+00 -0.0260531125
## [87,] 2.006292e-08 1.020791e+00 -0.0222653977
## [88,] 1.954302e-08 1.018959e+00 -0.0203945633
## [89,] -8.479765e-09 9.931087e-01 0.0075763780
## [90,] 2.931677e-09 1.006922e+00 -0.0071006405
## [91,] 4.287825e-09 1.005695e+00 -0.0059759917
## [92,] 1.422611e-08 1.014762e+00 -0.0157947433
## [93,] -1.005341e-08 9.910054e-01 0.0097986617
## [94,] -1.622328e-08 9.820903e-01 0.0191804775
## [95,] 2.457823e-09 1.005805e+00 -0.0059472013
## [96,] -1.182100e-08 9.884594e-01 0.0124783522
## [97,] -4.732675e-09 9.977892e-01 0.0026123826
## [98,] -6.463372e-09 9.957035e-01 0.0048290000
## [99,] -1.687834e-08 9.810711e-01 0.0202492197
## [100,] -5.068345e-09 9.975287e-01 0.0028982734
## [101,] 2.847919e-08 1.611746e-02 0.9816996989
## [102,] -1.304134e-08 -2.750699e-02 1.0284656607
## [103,] 1.774635e-08 7.414355e-04 0.9978874989
## [104,] -2.429532e-08 -4.175076e-02 1.0435607624
## [105,] 2.423892e-08 9.722515e-03 0.9884153315
## [106,] 2.594084e-08 1.214019e-02 0.9858689334
## [107,] -4.599434e-08 1.106034e-01 0.8928607528
## [108,] 2.783136e-09 -1.976362e-02 1.0195243612
## [109,] 5.496684e-09 -1.547119e-02 1.0150267162
## [110,] 2.697479e-08 1.381095e-02 0.9841199809
## [111,] -3.508921e-08 2.349229e-02 0.9791397841
## [112,] -1.302953e-08 -2.782615e-02 1.0287839066
## [113,] 7.447041e-09 -1.051014e-02 1.0099183104
## [114,] 8.970559e-09 -8.870366e-03 1.0081632651
## [115,] 2.632095e-08 1.290539e-02 0.9850750002
## [116,] 1.757437e-08 1.456074e-03 0.9971859363
## [117,] -4.661298e-08 -3.335133e-02 1.0368521661
## [118,] 2.144711e-08 5.494360e-03 0.9928546292
## [119,] 2.901731e-08 1.697594e-02 0.9808005253
## [120,] -6.154912e-08 1.369757e-01 0.8676682886
## [121,] 2.229383e-08 7.152460e-03 0.9911325189
## [122,] -8.600588e-09 -2.104019e-02 1.0216629943
## [123,] 2.577050e-08 1.185397e-02 0.9861680301
## [124,] -3.973496e-08 1.159811e-01 0.8870093798
## [125,] 5.867320e-09 -1.310172e-02 1.0126293446
## [126,] -4.112807e-08 -5.058601e-02 1.0536702249
## [127,] -2.230221e-08 2.589752e-01 0.7427050161
## [128,] -2.475588e-08 2.760088e-01 0.7258584628
## [129,] 2.019108e-08 4.079302e-03 0.9943647140
## [130,] -7.527091e-08 1.104602e-01 0.8952211679
## [131,] 8.937260e-09 -1.113945e-02 1.0104347093
## [132,] -2.291614e-08 -4.145052e-02 1.0431560877
## [133,] 2.431264e-08 9.879077e-03 0.9882531972
## [134,] 1.914722e-08 7.195858e-01 0.2789876376
## [135,] -9.596970e-08 5.440509e-02 0.9528399922
## [136,] 2.585065e-08 1.212061e-02 0.9858953367
## [137,] 2.474088e-08 1.056823e-02 0.9875316572
## [138,] -5.172362e-08 -2.823743e-02 1.0321256849
## [139,] -9.754643e-09 3.652060e-01 0.6355314174
## [140,] -3.843854e-09 -1.841194e-02 1.0186746795
## [141,] 2.590057e-08 1.225655e-02 0.9857556269
## [142,] 8.985900e-09 -5.395037e-03 1.0046870189
## [143,] -1.304134e-08 -2.750699e-02 1.0284656607
## [144,] 2.519174e-08 1.114099e-02 0.9869247933
## [145,] 2.710104e-08 1.402407e-02 0.9838973128
## [146,] 1.701386e-08 1.172762e-03 0.9975116788
## [147,] -1.814548e-08 -2.283359e-02 1.0241791545
## [148,] -2.072295e-08 -2.182977e-02 1.0233706144
## [149,] 1.731377e-08 8.890183e-04 0.9977726886
## [150,] -5.314676e-08 3.570322e-02 0.9682973178
##
##
## $weights
## $weights[[1]]
## $weights[[1]][[1]]
## [,1] [,2] [,3]
## [1,] -12.0243897 -23.856522 17.352575
## [2,] -0.8369312 -0.165147 1.295529
## [3,] -2.1596604 -19.994336 3.087727
## [4,] 2.5346690 16.474487 -3.954193
## [5,] 6.4882488 56.361775 -8.793004
##
## $weights[[1]][[2]]
## [,1] [,2] [,3]
## [1,] 9.999992e-01 -2.3969066 2.45818932
## [2,] 8.575603e-07 1.4343652 -1.49921218
## [3,] -1.000000e+00 0.9798511 0.02147428
## [4,] 8.106730e-07 2.3968482 -2.45807632
##
##
##
## $generalized.weights
## $generalized.weights[[1]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] -6.493546e-06 -1.675667e-05 1.966583e-05 5.034268e-05 1.144482e-04
## [2,] -2.259696e-05 -5.831276e-05 6.843524e-05 1.751930e-04 3.983271e-04
## [3,] -1.346245e-05 -3.474034e-05 4.077128e-05 1.043722e-04 2.372864e-04
## [4,] -3.015331e-05 -7.781299e-05 9.131965e-05 2.337802e-04 5.315610e-04
## [5,] -5.689083e-06 -1.468073e-05 1.722950e-05 4.410582e-05 1.002691e-04
## [6,] -1.667293e-05 -4.302517e-05 5.049425e-05 1.292629e-04 2.938865e-04
## [7,] -2.342627e-05 -6.045284e-05 7.094682e-05 1.816226e-04 4.129531e-04
## [8,] -1.128914e-05 -2.913198e-05 3.418935e-05 8.752265e-05 1.989738e-04
## [9,] -4.260907e-05 -1.099568e-04 1.290420e-04 3.303541e-04 7.512706e-04
## [10,] -1.226277e-05 -3.164458e-05 3.713802e-05 9.507157e-05 2.161320e-04
## [11,] -4.226239e-06 -1.090582e-05 1.279926e-05 3.276466e-05 7.448667e-05
## [12,] -1.719457e-05 -4.437150e-05 5.207402e-05 1.333082e-04 3.030691e-04
## [13,] -1.284253e-05 -3.314067e-05 3.889383e-05 9.956635e-05 2.263531e-04
## [14,] -9.123948e-06 -2.354457e-05 2.763205e-05 7.073598e-05 1.608100e-04
## [15,] -7.396253e-07 -1.908583e-06 2.239974e-06 5.733967e-06 1.303637e-05
## [16,] -2.654325e-06 -6.849453e-06 8.038683e-06 2.057794e-05 4.678308e-05
## [17,] -6.050257e-06 -1.561270e-05 1.832333e-05 4.690567e-05 1.066387e-04
## [18,] -1.242314e-05 -3.205826e-05 3.762370e-05 9.631415e-05 2.189692e-04
## [19,] -8.414416e-06 -2.171356e-05 2.548322e-05 6.523493e-05 1.483053e-04
## [20,] -8.374357e-06 -2.161018e-05 2.536190e-05 6.492434e-05 1.475994e-04
## [21,] -1.340948e-05 -3.460370e-05 4.061082e-05 1.039618e-04 2.363474e-04
## [22,] -1.988270e-05 -5.130817e-05 6.021507e-05 1.541482e-04 3.504812e-04
## [23,] -2.885056e-06 -7.444861e-06 8.737457e-06 2.236674e-05 5.084944e-05
## [24,] -1.494680e-04 -3.524411e-04 4.254901e-04 1.065205e-03 2.645172e-03
## [25,] -3.677228e-05 -9.489481e-05 1.113652e-04 2.851024e-04 6.482592e-04
## [26,] -3.449886e-05 -8.902715e-05 1.044801e-04 2.674723e-04 6.082036e-04
## [27,] -5.323252e-05 -1.373686e-04 1.612126e-04 4.127107e-04 9.387762e-04
## [28,] -7.694863e-06 -1.985674e-05 2.330404e-05 5.965639e-05 1.356213e-04
## [29,] -7.411760e-06 -1.912616e-05 2.244666e-05 5.746145e-05 1.306326e-04
## [30,] -2.879203e-05 -7.430012e-05 8.719701e-05 2.232262e-04 5.075490e-04
## [31,] -3.286293e-05 -8.480559e-05 9.952573e-05 2.547890e-04 5.793442e-04
## [32,] -2.956554e-05 -7.629500e-05 8.953920e-05 2.292185e-04 5.212370e-04
## [33,] -1.100879e-06 -2.840797e-06 3.334037e-06 8.534646e-06 1.940311e-05
## [34,] -1.024743e-06 -2.644326e-06 3.103458e-06 7.944376e-06 1.806145e-05
## [35,] -2.345985e-05 -6.053962e-05 7.104849e-05 1.818836e-04 4.135360e-04
## [36,] -8.129142e-06 -2.097737e-05 2.461927e-05 6.302311e-05 1.432787e-04
## [37,] -3.606189e-06 -9.305753e-06 1.092142e-05 2.795749e-05 6.355930e-05
## [38,] -3.233172e-06 -8.343199e-06 9.791731e-06 2.506569e-05 5.698348e-05
## [39,] -2.664949e-05 -6.877081e-05 8.070835e-05 2.066134e-04 4.697830e-04
## [40,] -1.038295e-05 -2.679349e-05 3.144495e-05 8.049696e-05 1.830013e-04
## [41,] -1.048368e-05 -2.705337e-05 3.175004e-05 8.127758e-05 1.847825e-04
## [42,] -2.099188e-04 -2.317608e-04 3.826874e-04 7.551074e-04 3.758357e-03
## [43,] -1.730380e-05 -4.465328e-05 5.240483e-05 1.341546e-04 3.050017e-04
## [44,] -1.567013e-04 -3.708930e-04 4.472224e-04 1.120680e-03 2.773494e-03
## [45,] -4.414573e-05 -1.139223e-04 1.336957e-04 3.422682e-04 7.783820e-04
## [46,] -4.700207e-05 -1.212919e-04 1.423452e-04 3.644087e-04 8.288205e-04
## [47,] -5.639761e-06 -1.455347e-05 1.708013e-05 4.372352e-05 9.939851e-05
## [48,] -1.885887e-05 -4.866631e-05 5.711439e-05 1.462114e-04 3.324158e-04
## [49,] -4.595116e-06 -1.185772e-05 1.391640e-05 3.562450e-05 8.098791e-05
## [50,] -1.087383e-05 -2.806022e-05 3.293159e-05 8.430266e-05 1.916552e-04
## [51,] 4.339998e+00 1.157118e+01 -1.309915e+01 -3.546761e+01 2.135951e+01
## [52,] -1.934263e+00 -5.233688e+00 5.828871e+00 1.618251e+01 1.097480e+00
## [53,] -7.446967e-01 -2.169593e+00 2.225574e+00 6.987537e+00 -5.137218e-01
## [54,] -1.573048e+00 -4.286211e+00 4.736766e+00 1.330690e+01 8.618184e-01
## [55,] -6.158163e-01 -1.830962e+00 1.835984e+00 5.958712e+00 -8.215136e-01
## [56,] -1.572123e+00 -4.356428e+00 4.725251e+00 1.365532e+01 6.479049e-01
## [57,] -6.202473e-01 -1.843307e+00 1.849294e+00 5.997524e+00 -8.207880e-01
## [58,] 6.251893e-02 1.625167e-01 -1.891975e-01 -4.905001e-01 -8.893243e-02
## [59,] 6.932506e+00 1.856847e+01 -2.091373e+01 -5.707160e+01 9.882090e+00
## [60,] -2.263914e+00 -6.094946e+00 6.825957e+00 1.879007e+01 1.272168e+00
## [61,] 2.537104e-01 6.644318e-01 -7.671994e-01 -2.014596e+00 -3.585444e-01
## [62,] -1.650277e+00 -4.463611e+00 4.973286e+00 1.379842e+01 9.656895e-01
## [63,] 2.492213e-01 6.534593e-01 -7.535306e-01 -1.982790e+00 -3.453947e-01
## [64,] -7.600461e-01 -2.236134e+00 2.268828e+00 7.238440e+00 -8.432804e-01
## [65,] 1.958839e-01 5.109027e-01 -5.925874e-01 -1.545189e+00 -2.850480e-01
## [66,] 1.511817e+00 3.999103e+00 -4.566826e+00 -1.219989e+01 -3.445128e+00
## [67,] -5.353448e-01 -1.659660e+00 1.587911e+00 5.512897e+00 -2.020120e+00
## [68,] 1.176561e-01 3.073074e-01 -3.558805e-01 -9.302492e-01 -1.620547e-01
## [69,] 6.441594e-01 9.903096e-01 -2.031504e+00 -1.702983e+00 2.479976e+00
## [70,] 2.783466e-01 7.297479e-01 -8.416015e-01 -2.214127e+00 -3.914664e-01
## [71,] 5.984102e+00 1.170876e+01 -1.857108e+01 -2.810862e+01 1.908136e+00
## [72,] 5.582901e-01 1.466734e+00 -1.687665e+00 -4.455900e+00 -8.675305e-01
## [73,] 3.025345e+00 5.758453e+00 -9.408199e+00 -1.342182e+01 1.963872e+00
## [74,] -1.036777e+01 -2.824671e+01 3.121984e+01 8.768855e+01 3.548624e+00
## [75,] 8.985176e-01 2.372758e+00 -2.714682e+00 -7.231034e+00 -1.487564e+00
## [76,] 5.072546e+00 1.349104e+01 -1.531414e+01 -4.129137e+01 9.985855e+00
## [77,] -8.760143e-01 -2.509477e+00 2.623150e+00 8.010589e+00 -1.961789e-01
## [78,] 2.089129e+00 3.962065e+00 -6.498487e+00 -9.197854e+00 1.999688e+00
## [79,] -6.417084e-01 -1.899776e+00 1.914159e+00 6.169241e+00 -7.672506e-01
## [80,] 3.417303e-02 8.866722e-02 -1.034357e-01 -2.673012e-01 -4.896989e-02
## [81,] 2.965581e-01 7.774525e-01 -8.966701e-01 -2.358791e+00 -4.209009e-01
## [82,] 1.058064e-01 2.758236e-01 -3.201021e-01 -8.339472e-01 -1.484903e-01
## [83,] 3.011675e-01 7.889052e-01 -9.106830e-01 -2.392361e+00 -4.335669e-01
## [84,] -1.060282e+00 -1.883353e+00 3.313436e+00 4.043734e+00 2.321323e+00
## [85,] -3.968794e-01 -1.342471e+00 1.163750e+00 4.635923e+00 -7.570677e+00
## [86,] -9.866263e-01 -2.744821e+00 2.964153e+00 8.622798e+00 3.285360e-01
## [87,] -1.057062e+00 -2.942177e+00 3.175596e+00 9.245254e+00 3.504239e-01
## [88,] -1.046231e+00 -2.929299e+00 3.140987e+00 9.235096e+00 2.573480e-01
## [89,] 8.074824e-01 2.131667e+00 -2.439722e+00 -6.495025e+00 -1.285994e+00
## [90,] -4.775664e+00 -1.281665e+01 1.440402e+01 3.943891e+01 2.007939e+00
## [91,] -3.200457e+00 -8.755179e+00 9.633069e+00 2.724328e+01 1.585641e+00
## [92,] -1.291500e+00 -3.584975e+00 3.881058e+00 1.124805e+01 4.903088e-01
## [93,] 5.724656e-01 1.507280e+00 -1.730120e+00 -4.585223e+00 -8.590580e-01
## [94,] 7.176019e-02 1.866121e-01 -2.171550e-01 -5.633608e-01 -1.020634e-01
## [95,] -5.494303e+00 -1.479208e+01 1.656591e+01 4.560283e+01 2.183820e+00
## [96,] 3.767060e-01 9.907493e-01 -1.138623e+00 -3.011863e+00 -5.268300e-01
## [97,] 1.964252e+00 5.220967e+00 -5.930509e+00 -1.597369e+01 -4.919805e+00
## [98,] 1.268504e+00 3.360103e+00 -3.831283e+00 -1.025905e+01 -2.351284e+00
## [99,] 3.820781e-02 9.907535e-02 -1.156555e-01 -2.985637e-01 -5.522937e-02
## [100,] 1.802939e+00 4.782890e+00 -5.444586e+00 -1.461627e+01 -4.452110e+00
## [101,] -2.116376e-02 -5.494076e-02 6.405558e-02 1.656804e-01 -5.972750e-02
## [102,] 1.761897e+00 4.931147e+00 -5.289782e+00 -1.554291e+01 2.034278e-01
## [103,] -4.786524e-01 -1.264456e+00 1.446093e+00 3.854300e+00 -1.460170e+01
## [104,] 1.193268e+00 3.321103e+00 -3.584804e+00 -1.043564e+01 2.344093e-01
## [105,] -1.598011e-01 -4.184620e-01 4.832294e-01 1.268737e+00 -5.728014e-01
## [106,] -1.009931e-01 -2.630253e-01 3.055701e-01 7.947821e-01 -3.313147e-01
## [107,] -6.035911e-01 -8.096811e-01 1.917758e+00 1.016530e+00 2.750184e+00
## [108,] -6.691676e+00 -1.777458e+01 2.020507e+01 5.436001e+01 1.089438e+00
## [109,] -3.021939e+00 -8.045902e+00 9.122265e+00 2.464167e+01 1.203282e+00
## [110,] -6.605055e-02 -1.723332e-01 1.998087e-01 5.213231e-01 -1.943746e-01
## [111,] 8.328979e-02 7.890875e-01 -1.833287e-01 -3.457764e+00 5.508669e+00
## [112,] 1.773302e+00 4.956009e+00 -5.324871e+00 -1.560896e+01 2.230998e-01
## [113,] -1.937994e+00 -5.228589e+00 5.841939e+00 1.613931e+01 1.232753e+00
## [114,] -1.514565e+00 -4.077457e+00 4.566592e+00 1.257022e+01 1.434386e+00
## [115,] -8.576574e-02 -2.246741e-01 2.593406e-01 6.813477e-01 -2.511744e-01
## [116,] -4.700220e-01 -1.253745e+00 1.418568e+00 3.844009e+00 -6.283627e+00
## [117,] 5.160558e-01 1.632849e+00 -1.526737e+00 -5.475827e+00 -1.486613e+00
## [118,] -2.802001e-01 -7.340257e-01 8.472754e-01 2.226022e+00 -1.558677e+00
## [119,] -5.781285e-03 -1.495599e-02 1.750426e-02 4.500345e-02 -1.638763e-02
## [120,] -6.285320e-01 -9.735539e-01 1.981347e+00 1.697271e+00 2.746653e+00
## [121,] -2.344063e-01 -6.175917e-01 7.083793e-01 1.879505e+00 -9.707461e-01
## [122,] 2.344331e+00 6.611569e+00 -7.032396e+00 -2.092743e+01 1.035943e-01
## [123,] -1.071644e-01 -2.789563e-01 3.242595e-01 8.426546e-01 -3.596124e-01
## [124,] -7.176253e-01 -1.001011e+00 2.275468e+00 1.396456e+00 2.613337e+00
## [125,] -2.666404e+00 -7.171209e+00 8.040388e+00 2.209477e+01 1.134283e+00
## [126,] 7.752206e-01 2.229544e+00 -2.320275e+00 -7.132023e+00 -1.517838e-01
## [127,] -2.765696e+00 -5.134306e+00 8.616338e+00 1.163354e+01 2.053734e+00
## [128,] -2.625166e+00 -4.910758e+00 8.174045e+00 1.122528e+01 2.047942e+00
## [129,] -3.360035e-01 -8.854411e-01 1.015387e+00 2.694962e+00 -2.197313e+00
## [130,] -4.565594e-01 -6.525155e-01 1.445792e+00 9.651521e-01 3.208272e+00
## [131,] -1.617995e+00 -4.296361e+00 4.885595e+00 1.313700e+01 1.520784e+00
## [132,] 1.259973e+00 3.491367e+00 -3.787046e+00 -1.094363e+01 2.884502e-01
## [133,] -1.563136e-01 -4.097157e-01 4.726370e-01 1.242940e+00 -5.469294e-01
## [134,] 3.362096e+00 6.366990e+00 -1.045932e+01 -1.475694e+01 1.960930e+00
## [135,] -2.348503e-01 -2.162342e-01 7.580366e-01 -8.838771e-02 5.470159e+00
## [136,] -1.024027e-01 -2.676804e-01 3.097171e-01 8.106939e-01 -3.214675e-01
## [137,] -1.396990e-01 -3.665149e-01 4.223586e-01 1.112532e+00 -4.599301e-01
## [138,] 4.109080e-01 1.375906e+00 -1.206567e+00 -4.731136e+00 -2.438318e+00
## [139,] -7.840704e+00 -1.515356e+01 2.435542e+01 3.590917e+01 1.944138e+00
## [140,] 4.883647e+00 1.359595e+01 -1.467096e+01 -4.272811e+01 3.470244e-01
## [141,] -9.987351e-02 -2.615495e-01 3.020099e-01 7.930240e-01 -3.039947e-01
## [142,] -1.364443e+00 -3.764743e+00 4.102982e+00 1.177212e+01 1.148684e+00
## [143,] 1.761897e+00 4.931147e+00 -5.289782e+00 -1.554291e+01 2.034278e-01
## [144,] -1.250008e-01 -3.270494e-01 3.780294e-01 9.910546e-01 -4.111842e-01
## [145,] -6.183972e-02 -1.614729e-01 1.870554e-01 4.887061e-01 -1.784834e-01
## [146,] -4.977980e-01 -1.334354e+00 1.501616e+00 4.103098e+00 -7.379966e+00
## [147,] 1.171441e+00 3.435042e+00 -3.498266e+00 -1.110031e+01 -5.641637e-01
## [148,] 1.007638e+00 3.007999e+00 -3.002708e+00 -9.809102e+00 -9.027441e-01
## [149,] -4.920876e-01 -1.309803e+00 1.485500e+00 4.010756e+00 -1.096453e+01
## [150,] -7.171160e-02 3.115763e-01 2.767904e-01 -1.876372e+00 5.179857e+00
## [,6] [,7] [,8] [,9] [,10]
## [1,] 2.953403e-04 -3.466081e-04 -8.873116e-04 6.185933e-05 1.596315e-04
## [2,] 1.027938e-03 -1.206336e-03 -3.088367e-03 2.152641e-04 5.555182e-04
## [3,] 6.123410e-04 -7.186240e-04 -1.839717e-03 1.282453e-04 3.309493e-04
## [4,] 1.371787e-03 -1.609833e-03 -4.121476e-03 2.872465e-04 7.412893e-04
## [5,] 2.587498e-04 -3.036665e-04 -7.773792e-04 5.419591e-05 1.398554e-04
## [6,] 7.584060e-04 -8.900378e-04 -2.278559e-03 1.588310e-04 4.098800e-04
## [7,] 1.065682e-03 -1.250631e-03 -3.201766e-03 2.231665e-04 5.759112e-04
## [8,] 5.134705e-04 -6.025942e-04 -1.542668e-03 1.075408e-04 2.775189e-04
## [9,] 1.938812e-03 -2.275220e-03 -5.825122e-03 4.059261e-04 1.047576e-03
## [10,] 5.577518e-04 -6.545575e-04 -1.675713e-03 1.168135e-04 3.014494e-04
## [11,] 1.922159e-04 -2.255841e-04 -5.774852e-04 4.026091e-05 1.038949e-04
## [12,] 7.821096e-04 -9.178466e-04 -2.349788e-03 1.637932e-04 4.226893e-04
## [13,] 5.841285e-04 -6.855124e-04 -1.754959e-03 1.223371e-04 3.157035e-04
## [14,] 4.149830e-04 -4.870150e-04 -1.246769e-03 8.691587e-05 2.242931e-04
## [15,] 3.364020e-05 -3.948094e-05 -1.010659e-04 7.046511e-06 1.818344e-05
## [16,] 1.207245e-04 -1.416835e-04 -3.626973e-04 2.528712e-05 6.525380e-05
## [17,] 2.751855e-04 -3.229571e-04 -8.267552e-04 5.763844e-05 1.487382e-04
## [18,] 5.650690e-04 -6.631507e-04 -1.697688e-03 1.183465e-04 3.054032e-04
## [19,] 3.827122e-04 -4.491444e-04 -1.149812e-03 8.015769e-05 2.068524e-04
## [20,] 3.808906e-04 -4.470068e-04 -1.144339e-03 7.977622e-05 2.058679e-04
## [21,] 6.099203e-04 -7.157803e-04 -1.832448e-03 1.277380e-04 3.296415e-04
## [22,] 9.044569e-04 -1.061435e-03 -2.717360e-03 1.894118e-04 4.887982e-04
## [23,] 1.312181e-04 -1.539985e-04 -3.942240e-04 2.748502e-05 7.092564e-05
## [24,] 6.826784e-03 -8.010850e-03 -2.051163e-02 1.427770e-03 3.684847e-03
## [25,] 1.672980e-03 -1.963249e-03 -5.026455e-03 3.502874e-04 9.039941e-04
## [26,] 1.569585e-03 -1.841944e-03 -4.715762e-03 3.286494e-04 8.481405e-04
## [27,] 2.422710e-03 -2.843080e-03 -7.278989e-03 5.071868e-04 1.308900e-03
## [28,] 3.499803e-04 -4.107310e-04 -1.051473e-03 7.330264e-05 1.891624e-04
## [29,] 3.371057e-04 -3.956225e-04 -1.012791e-03 7.060639e-05 1.822042e-04
## [30,] 1.309821e-03 -1.537112e-03 -3.935300e-03 2.742745e-04 7.078129e-04
## [31,] 1.495107e-03 -1.754543e-03 -4.491997e-03 3.130599e-04 8.079087e-04
## [32,] 1.345125e-03 -1.578569e-03 -4.041331e-03 2.816682e-04 7.268830e-04
## [33,] 5.006982e-05 -5.876271e-05 -1.504263e-04 1.048789e-05 2.706404e-05
## [34,] 4.660755e-05 -5.469951e-05 -1.400243e-04 9.762689e-06 2.519259e-05
## [35,] 1.067191e-03 -1.252395e-03 -3.206306e-03 2.234817e-04 5.767268e-04
## [36,] 3.697398e-04 -4.339216e-04 -1.110836e-03 7.744105e-05 1.998414e-04
## [37,] 1.640166e-04 -1.924905e-04 -4.927630e-04 3.435471e-05 8.865328e-05
## [38,] 1.470480e-04 -1.725755e-04 -4.417841e-04 3.080052e-05 7.948182e-05
## [39,] 1.212348e-03 -1.422739e-03 -3.642429e-03 2.538708e-04 6.551522e-04
## [40,] 4.722508e-04 -5.542215e-04 -1.418826e-03 9.890887e-05 2.552427e-04
## [41,] 4.768449e-04 -5.596160e-04 -1.432624e-03 9.987134e-05 2.577252e-04
## [42,] 9.700032e-03 -1.138208e-02 -2.914507e-02 2.027404e-03 5.232555e-03
## [43,] 7.870939e-04 -9.236998e-04 -2.364757e-03 1.648374e-04 4.253822e-04
## [44,] 7.157910e-03 -8.399479e-03 -2.150642e-02 1.496926e-03 3.863298e-03
## [45,] 2.008781e-03 -2.357327e-03 -6.035349e-03 4.205688e-04 1.085365e-03
## [46,] 2.138936e-03 -2.510081e-03 -6.426373e-03 4.478082e-04 1.155656e-03
## [47,] 2.565038e-04 -3.010298e-04 -7.706323e-04 5.372541e-05 1.386415e-04
## [48,] 8.578421e-04 -1.006723e-03 -2.577320e-03 1.796507e-04 4.636113e-04
## [49,] 2.089930e-04 -2.452732e-04 -6.278901e-04 4.377477e-05 1.129627e-04
## [50,] 4.945830e-04 -5.804300e-04 -1.485920e-03 1.035857e-04 2.673116e-04
## [51,] 5.997612e+01 -6.410465e+01 -1.893856e+02 -3.881821e+01 -1.086487e+02
## [52,] 3.307024e+00 -3.266732e+00 -1.083468e+01 -1.139592e+00 -3.405433e+00
## [53,] -3.071802e-01 1.678066e+00 -1.005477e+00 3.930933e-01 7.121993e-02
## [54,] 2.726094e+00 -2.549760e+00 -9.140869e+00 -9.008788e-01 -2.812628e+00
## [55,] -1.043559e+00 2.617167e+00 1.097260e+00 6.720272e-01 7.467384e-01
## [56,] 2.519296e+00 -1.860483e+00 -9.173175e+00 -7.119482e-01 -2.649387e+00
## [57,] -1.035658e+00 2.615693e+00 1.062111e+00 6.707447e-01 7.379967e-01
## [58,] -2.327167e-01 2.689465e-01 7.052659e-01 8.723735e-02 2.282107e-01
## [59,] 2.826964e+01 -2.959577e+01 -9.017378e+01 -1.236130e+01 -3.520816e+01
## [60,] 3.727869e+00 -3.799369e+00 -1.204236e+01 -1.318056e+00 -3.839035e+00
## [61,] -9.538304e-01 1.082426e+00 2.919781e+00 3.508759e-01 9.326953e-01
## [62,] 2.903336e+00 -2.875234e+00 -9.501449e+00 -1.000031e+00 -2.982231e+00
## [63,] -9.215430e-01 1.042404e+00 2.825894e+00 3.383855e-01 9.020425e-01
## [64,] -8.569983e-01 2.712223e+00 7.719741e-02 6.670557e-01 5.178348e-01
## [65,] -7.512234e-01 8.613948e-01 2.286565e+00 2.787499e-01 7.342583e-01
## [66,] -9.417594e+00 1.037034e+01 2.929216e+01 3.175454e+00 8.664390e+00
## [67,] -3.401159e+00 6.335444e+00 6.787877e+00 1.650061e+00 2.670010e+00
## [68,] -4.284448e-01 4.895544e-01 1.306619e+00 1.590934e-01 4.203663e-01
## [69,] 5.496311e+00 -7.619082e+00 -1.480250e+01 -2.565306e+00 -5.669987e+00
## [70,] -1.044191e+00 1.181482e+00 3.201485e+00 3.830681e-01 1.020894e+00
## [71,] 4.310393e+00 -5.852475e+00 -1.178816e+01 -1.933686e+00 -4.360492e+00
## [72,] -2.326244e+00 2.616822e+00 7.154621e+00 8.406340e-01 2.251729e+00
## [73,] 4.421484e+00 -6.025204e+00 -1.205993e+01 -1.994401e+00 -4.481682e+00
## [74,] 1.121493e+01 -1.050010e+01 -3.758929e+01 -3.845395e+00 -1.199611e+01
## [75,] -4.045803e+00 4.480257e+00 1.254711e+01 1.427676e+00 3.876619e+00
## [76,] 2.778852e+01 -2.999992e+01 -8.731043e+01 -1.271338e+01 -3.528241e+01
## [77,] 4.147060e-01 7.046733e-01 -2.989593e+00 1.032580e-01 -5.953712e-01
## [78,] 4.500294e+00 -6.135308e+00 -1.227092e+01 -2.033417e+00 -4.567413e+00
## [79,] -9.068096e-01 2.452437e+00 6.926250e-01 6.225325e-01 6.205227e-01
## [80,] -1.276659e-01 1.481504e-01 3.860099e-01 4.804048e-02 1.252157e-01
## [81,] -1.122558e+00 1.270336e+00 3.441492e+00 4.115639e-01 1.096699e+00
## [82,] -3.909021e-01 4.487792e-01 1.189020e+00 1.456641e-01 3.832825e-01
## [83,] -1.154082e+00 1.308834e+00 3.534005e+00 4.235898e-01 1.126616e+00
## [84,] 5.191546e+00 -7.126036e+00 -1.408501e+01 -2.379884e+00 -5.310645e+00
## [85,] -1.448289e+01 2.353450e+01 3.394373e+01 5.261574e+00 9.897112e+00
## [86,] 1.392684e+00 -9.295743e-01 -5.215765e+00 -3.711044e-01 -1.479002e+00
## [87,] 1.503727e+00 -9.893132e-01 -5.652679e+00 -3.972864e-01 -1.598421e+00
## [88,] 1.350651e+00 -6.969757e-01 -5.357709e+00 -3.132927e-01 -1.462073e+00
## [89,] -3.494277e+00 3.873564e+00 1.083074e+01 1.239408e+00 3.362364e+00
## [90,] 5.794797e+00 -6.007472e+00 -1.857068e+01 -2.105337e+00 -6.045900e+00
## [91,] 5.190782e+00 -4.670233e+00 -1.767567e+01 -1.683433e+00 -5.417901e+00
## [92,] 1.973709e+00 -1.399874e+00 -7.271049e+00 -5.444706e-01 -2.083356e+00
## [93,] -2.316998e+00 2.589649e+00 7.150731e+00 8.340704e-01 2.246720e+00
## [94,] -2.672924e-01 3.086309e-01 8.104514e-01 1.001050e-01 2.620774e-01
## [95,] 6.399826e+00 -6.521987e+00 -2.067460e+01 -2.302029e+00 -6.705504e+00
## [96,] -1.416684e+00 1.588650e+00 4.364480e+00 5.150341e-01 1.383348e+00
## [97,] -1.366147e+01 1.478380e+01 4.287235e+01 4.435073e+00 1.228334e+01
## [98,] -6.455056e+00 7.074396e+00 2.012690e+01 2.222171e+00 6.088134e+00
## [99,] -1.438118e-01 1.671082e-01 4.345046e-01 5.415607e-02 1.409904e-01
## [100,] -1.228170e+01 1.338812e+01 3.839972e+01 4.037010e+00 1.111126e+01
## [101,] -1.558693e-01 1.806769e-01 4.715812e-01 5.525739e-02 1.441690e-01
## [102,] 1.049700e+00 -5.530992e-01 -4.147190e+00 -2.558215e-01 -1.179695e+00
## [103,] -3.975514e+01 4.397245e+01 1.233670e+02 5.436691e+00 1.477744e+01
## [104,] 1.004446e+00 -6.619553e-01 -3.774180e+00 -2.725640e-01 -1.095402e+00
## [105,] -1.523513e+00 1.729292e+00 4.663089e+00 5.072189e-01 1.348026e+00
## [106,] -8.704028e-01 1.001540e+00 2.644217e+00 2.994340e-01 7.863246e-01
## [107,] 6.062876e+00 -8.453100e+00 -1.625718e+01 -2.849871e+00 -6.263668e+00
## [108,] 3.018254e+00 -3.274545e+00 -9.459669e+00 -1.173828e+00 -3.243960e+00
## [109,] 3.361485e+00 -3.613389e+00 -1.058449e+01 -1.321809e+00 -3.681786e+00
## [110,] -5.126585e-01 5.873385e-01 1.561162e+00 1.780268e-01 4.692965e-01
## [111,] 1.161827e+01 -1.699482e+01 -2.998832e+01 -6.175787e+00 -1.294547e+01
## [112,] 1.087660e+00 -6.142130e-01 -4.236991e+00 -2.745537e-01 -1.215569e+00
## [113,] 3.653092e+00 -3.676770e+00 -1.186869e+01 -1.416108e+00 -4.167475e+00
## [114,] 4.202813e+00 -4.283887e+00 -1.357592e+01 -1.684645e+00 -4.906342e+00
## [115,] -6.686679e-01 7.582250e-01 2.047734e+00 2.292448e-01 6.097930e-01
## [116,] -1.767539e+01 1.885480e+01 5.586789e+01 3.478459e+00 9.752217e+00
## [117,] -2.631697e+00 4.646815e+00 5.625914e+00 1.293073e+00 2.222626e+00
## [118,] -4.149546e+00 4.705198e+00 1.270777e+01 1.264592e+00 3.363895e+00
## [119,] -4.248112e-02 4.960716e-02 1.279923e-01 1.519627e-02 3.938921e-02
## [120,] 6.089551e+00 -8.438112e+00 -1.640507e+01 -2.853145e+00 -6.308603e+00
## [121,] -2.623009e+00 2.925762e+00 8.103787e+00 8.293301e-01 2.237862e+00
## [122,] 9.327051e-01 -2.338720e-01 -4.061954e+00 -1.695432e-01 -1.099858e+00
## [123,] -9.437273e-01 1.087204e+00 2.865081e+00 3.241170e-01 8.502516e-01
## [124,] 5.768737e+00 -8.031575e+00 -1.548518e+01 -2.694818e+00 -5.931091e+00
## [125,] 3.306864e+00 -3.389608e+00 -1.065408e+01 -1.269822e+00 -3.681082e+00
## [126,] 1.325849e-01 5.226080e-01 -1.390947e+00 9.993274e-02 -2.473966e-01
## [127,] 4.611525e+00 -6.302373e+00 -1.255164e+01 -2.086769e+00 -4.676195e+00
## [128,] 4.602099e+00 -6.284170e+00 -1.253377e+01 -2.081177e+00 -4.667470e+00
## [129,] -5.940437e+00 6.622170e+00 1.835873e+01 1.684674e+00 4.548257e+00
## [130,] 7.088324e+00 -9.859233e+00 -1.904137e+01 -3.388279e+00 -7.464382e+00
## [131,] 4.208649e+00 -4.571607e+00 -1.318237e+01 -1.728384e+00 -4.771524e+00
## [132,] 1.121124e+00 -8.283530e-01 -4.081600e+00 -3.251529e-01 -1.209580e+00
## [133,] -1.458035e+00 1.650784e+00 4.468804e+00 4.855990e-01 1.293428e+00
## [134,] 4.412357e+00 -6.016476e+00 -1.202960e+01 -1.991156e+00 -4.471733e+00
## [135,] 1.196562e+01 -1.682457e+01 -3.187767e+01 -6.300089e+00 -1.373292e+01
## [136,] -8.514583e-01 9.709413e-01 2.599545e+00 2.912018e-01 7.707951e-01
## [137,] -1.229000e+00 1.387849e+00 3.772122e+00 4.118211e-01 1.099414e+00
## [138,] -4.629808e+00 7.584023e+00 1.076218e+01 2.086433e+00 3.891282e+00
## [139,] 4.384905e+00 -5.963716e+00 -1.197719e+01 -1.970681e+00 -4.436701e+00
## [140,] 1.497896e+00 -9.786650e-01 -5.640727e+00 -4.167647e-01 -1.684397e+00
## [141,] -8.086748e-01 9.177477e-01 2.475374e+00 2.760332e-01 7.337158e-01
## [142,] 4.158587e+00 -3.335448e+00 -1.475520e+01 -1.520234e+00 -5.333907e+00
## [143,] 1.049700e+00 -5.530992e-01 -4.147190e+00 -2.558215e-01 -1.179695e+00
## [144,] -1.091402e+00 1.241638e+00 3.336377e+00 3.695012e-01 9.800631e-01
## [145,] -4.715690e-01 5.392214e-01 1.437560e+00 1.637727e-01 4.324541e-01
## [146,] -2.118267e+01 2.209368e+01 6.768894e+01 3.740990e+00 1.068870e+01
## [147,] -5.089352e-01 1.822237e+00 -2.637935e-01 4.670217e-01 2.893208e-01
## [148,] -1.209262e+00 2.868446e+00 1.511948e+00 7.757733e-01 9.303637e-01
## [149,] -3.059841e+01 3.292971e+01 9.629074e+01 4.672339e+00 1.300153e+01
## [150,] 1.109973e+01 -1.595940e+01 -2.905520e+01 -5.818392e+00 -1.240703e+01
## [,11] [,12]
## [1,] -1.873419e-04 -4.795919e-04
## [2,] -6.519285e-04 -1.669013e-03
## [3,] -3.883921e-04 -9.943034e-04
## [4,] -8.699263e-04 -2.227169e-03
## [5,] -1.641331e-04 -4.201766e-04
## [6,] -4.810210e-04 -1.231445e-03
## [7,] -6.758610e-04 -1.730282e-03
## [8,] -3.256886e-04 -8.337760e-04
## [9,] -1.229346e-03 -3.147417e-03
## [10,] -3.537707e-04 -9.056758e-04
## [11,] -1.219309e-04 -3.121372e-04
## [12,] -4.960488e-04 -1.269936e-03
## [13,] -3.704989e-04 -9.485006e-04
## [14,] -2.632258e-04 -6.738624e-04
## [15,] -2.134052e-05 -5.462882e-05
## [16,] -7.658256e-05 -1.960445e-04
## [17,] -1.745590e-04 -4.468624e-04
## [18,] -3.584138e-04 -9.175497e-04
## [19,] -2.427586e-04 -6.214625e-04
## [20,] -2.416034e-04 -6.185046e-04
## [21,] -3.868557e-04 -9.903762e-04
## [22,] -5.736351e-04 -1.468549e-03
## [23,] -8.323890e-05 -2.130848e-04
## [24,] -4.323976e-03 -1.107140e-02
## [25,] -1.060844e-03 -2.716040e-03
## [26,] -9.953146e-04 -2.548206e-03
## [27,] -1.536014e-03 -3.932562e-03
## [28,] -2.219980e-04 -5.683151e-04
## [29,] -2.138325e-04 -5.474092e-04
## [30,] -8.306404e-04 -2.126591e-03
## [31,] -9.481016e-04 -2.427331e-03
## [32,] -8.530336e-04 -2.183866e-03
## [33,] -3.176278e-05 -8.130929e-05
## [34,] -2.956652e-05 -7.568673e-05
## [35,] -6.768153e-04 -1.732737e-03
## [36,] -2.345313e-04 -6.003978e-04
## [37,] -1.040439e-04 -2.663452e-04
## [38,] -9.327991e-05 -2.387914e-04
## [39,] -7.688486e-04 -1.968364e-03
## [40,] -2.995466e-04 -7.668484e-04
## [41,] -3.024616e-04 -7.743043e-04
## [42,] -6.139937e-03 -1.572189e-02
## [43,] -4.992112e-04 -1.278024e-03
## [44,] -4.533416e-03 -1.160751e-02
## [45,] -1.273691e-03 -3.260959e-03
## [46,] -1.356186e-03 -3.472132e-03
## [47,] -1.627082e-04 -4.165302e-04
## [48,] -5.440732e-04 -1.392883e-03
## [49,] -1.325726e-04 -3.393805e-04
## [50,] -3.137104e-04 -8.031078e-04
## [51,] 1.165441e+02 3.424687e+02
## [52,] 3.395498e+00 1.111091e+01
## [53,] -1.303699e+00 1.571768e+00
## [54,] 2.669767e+00 9.373844e+00
## [55,] -2.153770e+00 -3.738904e-01
## [56,] 2.058662e+00 9.497421e+00
## [57,] -2.150538e+00 -3.373426e-01
## [58,] -2.638288e-01 -6.914787e-01
## [59,] 3.703918e+01 1.120435e+02
## [60,] 3.939211e+00 1.236262e+01
## [61,] -1.059363e+00 -2.853734e+00
## [62,] 2.980405e+00 9.720064e+00
## [63,] -1.021346e+00 -2.764632e+00
## [64,] -2.164649e+00 7.229174e-01
## [65,] -8.424063e-01 -2.234246e+00
## [66,] -9.560501e+00 -2.692078e+01
## [67,] -5.187848e+00 -5.014982e+00
## [68,] -4.806383e-01 -1.281522e+00
## [69,] 7.883088e+00 1.523621e+01
## [70,] -1.156243e+00 -3.128417e+00
## [71,] 5.931754e+00 1.190869e+01
## [72,] -2.535979e+00 -6.921082e+00
## [73,] 6.119891e+00 1.220560e+01
## [74,] 1.139703e+01 3.996528e+01
## [75,] -4.300641e+00 -1.201110e+01
## [76,] 3.820559e+01 1.106870e+02
## [77,] -4.161645e-01 3.420441e+00
## [78,] 6.239847e+00 1.243486e+01
## [79,] -2.003694e+00 2.452588e-03
## [80,] -1.453419e-01 -3.785505e-01
## [81,] -1.242270e+00 -3.360462e+00
## [82,] -4.402590e-01 -1.165510e+00
## [83,] -1.278825e+00 -3.448229e+00
## [84,] 7.307232e+00 1.438220e+01
## [85,] -1.637655e+01 -2.276588e+01
## [86,] 1.061318e+00 5.430538e+00
## [87,] 1.134386e+00 5.887495e+00
## [88,] 8.703595e-01 5.630085e+00
## [89,] -3.733881e+00 -1.041229e+01
## [90,] 6.302472e+00 1.932463e+01
## [91,] 4.969426e+00 1.831024e+01
## [92,] 1.567519e+00 7.543442e+00
## [93,] -2.514669e+00 -6.928616e+00
## [94,] -3.027193e-01 -7.944784e-01
## [95,] 6.879906e+00 2.159417e+01
## [96,] -1.553274e+00 -4.258845e+00
## [97,] -1.333105e+01 -3.849101e+01
## [98,] -6.687425e+00 -1.896065e+01
## [99,] -1.638639e-01 -4.259300e-01
## [100,] -1.214290e+01 -3.469538e+01
## [101,] -1.671589e-01 -4.361169e-01
## [102,] 7.123997e-01 4.527881e+00
## [103,] -1.637535e+01 -4.581260e+01
## [104,] 7.784081e-01 4.033236e+00
## [105,] -1.531425e+00 -4.124033e+00
## [106,] -9.052057e-01 -2.388192e+00
## [107,] 8.761778e+00 1.675354e+01
## [108,] 3.529171e+00 1.015279e+01
## [109,] 3.970614e+00 1.157412e+01
## [110,] -5.379699e-01 -1.428661e+00
## [111,] 1.906253e+01 3.322911e+01
## [112,] 7.706266e-01 4.612059e+00
## [113,] 4.227115e+00 1.349214e+01
## [114,] 5.034874e+00 1.579886e+01
## [115,] -6.920851e-01 -1.866527e+00
## [116,] -1.044144e+01 -3.076819e+01
## [117,] -4.049833e+00 -4.568007e+00
## [118,] -3.817767e+00 -1.029674e+01
## [119,] -4.600120e-02 -1.186699e-01
## [120,] 8.767316e+00 1.695762e+01
## [121,] -2.499908e+00 -6.908393e+00
## [122,] 4.339632e-01 4.558404e+00
## [123,] -9.799307e-01 -2.580690e+00
## [124,] 8.284092e+00 1.588224e+01
## [125,] 3.797156e+00 1.182467e+01
## [126,] -3.632964e-01 1.699923e+00
## [127,] 6.404893e+00 1.270697e+01
## [128,] 6.387270e+00 1.269156e+01
## [129,] -5.077952e+00 -1.404493e+01
## [130,] 1.041500e+01 2.000370e+01
## [131,] 5.197066e+00 1.492487e+01
## [132,] 9.402586e-01 4.335508e+00
## [133,] -1.465805e+00 -3.962257e+00
## [134,] 6.110252e+00 1.217273e+01
## [135,] 1.938297e+01 3.647848e+01
## [136,] -8.795886e-01 -2.352354e+00
## [137,] -1.242803e+00 -3.372501e+00
## [138,] -6.497982e+00 -8.864355e+00
## [139,] 6.046108e+00 1.210118e+01
## [140,] 1.189090e+00 6.213413e+00
## [141,] -8.334024e-01 -2.244863e+00
## [142,] 4.434707e+00 1.869622e+01
## [143,] 7.123997e-01 4.527881e+00
## [144,] -1.115854e+00 -2.994727e+00
## [145,] -4.948081e-01 -1.317862e+00
## [146,] -1.120543e+01 -3.407211e+01
## [147,] -1.524312e+00 8.647783e-01
## [148,] -2.478061e+00 -7.663458e-01
## [149,] -1.403690e+01 -4.084922e+01
## [150,] 1.793408e+01 3.233814e+01
##
##
## $startweights
## $startweights[[1]]
## $startweights[[1]][[1]]
## [,1] [,2] [,3]
## [1,] 1.2629543 -1.539950042 0.7635935
## [2,] -0.3262334 -0.928567035 -0.7990092
## [3,] 1.3297993 -0.294720447 -1.1476570
## [4,] 1.2724293 -0.005767173 -0.2894616
## [5,] 0.4146414 2.404653389 -0.2992151
##
## $startweights[[1]][[2]]
## [,1] [,2] [,3]
## [1,] -0.4115108 -1.2375384 0.80418951
## [2,] 0.2522234 -0.2242679 -0.05710677
## [3,] -0.8919211 0.3773956 0.50360797
## [4,] 0.4356833 0.1333364 1.08576936
##
##
##
## $result.matrix
## [,1]
## error 1.934716e+00
## reached.threshold 9.909091e-03
## steps 2.665400e+04
## Intercept.to.1layhid1 -1.202439e+01
## Sepal.Length.to.1layhid1 -8.369312e-01
## Sepal.Width.to.1layhid1 -2.159660e+00
## Petal.Length.to.1layhid1 2.534669e+00
## Petal.Width.to.1layhid1 6.488249e+00
## Intercept.to.1layhid2 -2.385652e+01
## Sepal.Length.to.1layhid2 -1.651470e-01
## Sepal.Width.to.1layhid2 -1.999434e+01
## Petal.Length.to.1layhid2 1.647449e+01
## Petal.Width.to.1layhid2 5.636178e+01
## Intercept.to.1layhid3 1.735257e+01
## Sepal.Length.to.1layhid3 1.295529e+00
## Sepal.Width.to.1layhid3 3.087727e+00
## Petal.Length.to.1layhid3 -3.954193e+00
## Petal.Width.to.1layhid3 -8.793004e+00
## Intercept.to.setosa 9.999992e-01
## 1layhid1.to.setosa 8.575603e-07
## 1layhid2.to.setosa -1.000000e+00
## 1layhid3.to.setosa 8.106730e-07
## Intercept.to.versicolor -2.396907e+00
## 1layhid1.to.versicolor 1.434365e+00
## 1layhid2.to.versicolor 9.798511e-01
## 1layhid3.to.versicolor 2.396848e+00
## Intercept.to.virginica 2.458189e+00
## 1layhid1.to.virginica -1.499212e+00
## 1layhid2.to.virginica 2.147428e-02
## 1layhid3.to.virginica -2.458076e+00
##
## attr(,"class")
## [1] "nn"Plot for Iris NN
Plotting the Neural Network:
plot(nn_iris, rep="best")
NN on Iris data using caret
Now, doing the same thing using caret:
set.seed(0)
nn_caret <- caret::train(Species~., data = iris,
method = "nnet", linout = TRUE,
trace = FALSE)
ps <- predict(nn_caret, iris)
confusionMatrix(ps, iris$Species)$overall["Accuracy"]## Accuracy
## 0.9733333Plot caret NN
Plotting the `caret’ neural network:
NeuralNetTools::plotnet(nn_caret) 
Additional practice
The TBnanostring.rds dataset contains gene expression
measurements in the blood for 107 TB-related genes for 179 patients with
either active tuberculosis infection (TB) or latent TB infection (LTBI)
from one of Dr. Johnson’s
publications. When you Load these data into R (
TBnanostring <- readRDS("TBnanostring.rds")) the TB
status is found in the first column of the data frame, followed by the
genes in the subsequent columns. The rows represent each individual
patient.
Here is a UMAP clustering of the dataset, and plot the result using
ggplot. The points are colored based on TB status.
Split the dataset into “training” and “testing” sets using a 70/30
partition, using set.seed(0) and the
createDataPartition function from the caret
package (code is ‘hiding’ in the .Rmd file!). Apply the
following machine learning methods to make a predictive biomarker to
distinguish between the TB and control samples, use the
caret package and cross validation to find the “finalModel”
parameters to for each method.
Now, using the caret::train() function, apply the
following machine learning methods to make a predictive biomarker to
distinguish between the TB and control samples, use the
caret package and cross validation to find the “finalModel”
parameters to for each method. Provide any relevant/informative plots
with your results.
- Split the dataset into “training” and “testing” sets using a 70/30
partition (use
set.seed(0)and thecaret::createDataPartition). - Apply a Support Vector Machine to these data (try linear, radial, and polynomial kernels).
- Apply a Random Forest Model to these data.
- Apply a Feedforward Perceptron Neural Network to these data.
- Compare the overall accuracy of the prediction methods for each of the machine learning tools in the previous problem. Which one performs the best?
(Note: the TBnanostring.Rmd and
TBnanostring.html files provide suggested solutions for
these analyses)
Session Info
sessionInfo()## R version 4.4.0 (2024-04-24)
## Platform: aarch64-apple-darwin20
## Running under: macOS Sonoma 14.2.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: Africa/Kampala
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] neuralnet_1.44.2 randomForest_4.7-1.2 mda_0.5-4
## [4] class_7.3-22 gridExtra_2.3 e1071_1.7-16
## [7] lubridate_1.9.3 forcats_1.0.0 stringr_1.5.1
## [10] dplyr_1.1.4 purrr_1.0.2 readr_2.1.5
## [13] tidyr_1.3.1 tibble_3.2.1 tidyverse_2.0.0
## [16] DT_0.33 caret_6.0-94 lattice_0.22-6
## [19] ggplot2_3.5.1 umap_0.2.10.0
##
## loaded via a namespace (and not attached):
## [1] tidyselect_1.2.1 timeDate_4041.110 farver_2.1.2
## [4] fastmap_1.2.0 pROC_1.18.5 digest_0.6.37
## [7] rpart_4.1.23 timechange_0.3.0 lifecycle_1.0.4
## [10] survival_3.7-0 magrittr_2.0.3 compiler_4.4.0
## [13] rlang_1.1.4 sass_0.4.9 tools_4.4.0
## [16] utf8_1.2.4 yaml_2.3.10 data.table_1.16.0
## [19] knitr_1.48 labeling_0.4.3 askpass_1.2.0
## [22] htmlwidgets_1.6.4 reticulate_1.39.0 plyr_1.8.9
## [25] withr_3.0.1 nnet_7.3-19 grid_4.4.0
## [28] stats4_4.4.0 fansi_1.0.6 colorspace_2.1-1
## [31] future_1.34.0 globals_0.16.3 scales_1.3.0
## [34] iterators_1.0.14 MASS_7.3-61 cli_3.6.3
## [37] rmarkdown_2.28 generics_0.1.3 rstudioapi_0.16.0
## [40] future.apply_1.11.2 RSpectra_0.16-2 tzdb_0.4.0
## [43] reshape2_1.4.4 proxy_0.4-27 cachem_1.1.0
## [46] splines_4.4.0 parallel_4.4.0 vctrs_0.6.5
## [49] hardhat_1.4.0 Matrix_1.7-0 jsonlite_1.8.9
## [52] hms_1.1.3 listenv_0.9.1 crosstalk_1.2.1
## [55] foreach_1.5.2 gower_1.0.1 jquerylib_0.1.4
## [58] recipes_1.1.0 glue_1.8.0 parallelly_1.38.0
## [61] codetools_0.2-20 stringi_1.8.4 gtable_0.3.5
## [64] munsell_0.5.1 pillar_1.9.0 htmltools_0.5.8.1
## [67] ipred_0.9-15 openssl_2.2.2 lava_1.8.0
## [70] R6_2.5.1 NeuralNetTools_1.5.3 evaluate_1.0.0
## [73] highr_0.11 png_0.1-8 bslib_0.8.0
## [76] Rcpp_1.0.13 nlme_3.1-166 prodlim_2024.06.25
## [79] xfun_0.47 pkgconfig_2.0.3 ModelMetrics_1.2.2.2